There's no flaws in your experiment.

Sadly, I know quite few about how pilots actually operate these machines, but mainly focused on the 'back-end' of them. And the operations can be mostly customized by the softwares, so I can't tell the procedure is right or not. Anyway it's quite reasonable.
In general, This require the on-board computer to compute separated dynamic/kinematic prediction/calculation for two pairs of target and missile, so after finishing the first, your jet still 'remember' the shared 'coordinate system', and send correction to the missile, also doing the illumination.
Thank you very much for your answer. This is some insight, even if you are not familiar with details.
Generally, summarize :
1. It have to be some mode, supported by software. Actual implementation depends on software "package" implemented
2. Targeting solution is prepared and kept in memory , for two targets (pair target - missile(s))
3. This may have little practical value - as it may required specific tactical situation to be successful
This is my understanding:
In minimum (the lest chances from described single target track - single target engaged) implementation:
1. Targets are observed in SNP. System estimate distances, closures rates and effective ranges R-27R(E)
2. System or pilot selects at least one (or maybe two) to be engaged.
3. When first target is in range. Pilot press zahvat button (or lock is done automatically) - the first is locked. Firing solution (precise position and vector) is being developed. Rough position and vector (from SNP) for the second target in this time is extrapolated in memory.
4. Pilot launches missile against the first target. System works for a while, for the the first target - as we know, tracking target and providing corrections.
Points 3, 4 takes several of seconds, minimum. Let say five to seven. More if required by separation in time. Even more - if the second target wants to be locked when in optimum distance to immediately launch missile.
For all this time - the second target is assumed straight flight - and its position is only extrapolated
5. After some time (separation in time) - required, and assumed, pilot (or system), switches to the second target. Its position is somehow extrapolated, so if separation in time is low (couple of seconds), and if target has not changed trajectory significantly - its position is somehow known. Radar searches in that area. Gets lock. Firing solution (precise position and vector) is being developed.
6. If target is within range, pilot launches missile. System works for a while, for the the second target - as we know, tracking target and providing corrections. Position of the first target in this time is only extrapolated. Missile for the first target get no corrections and fly to assumed position using only INS.
Again , points 5, 6 takes in minimum case several seconds. Maybe more if decided.
7. Radar switches to the first target.
This may be immediately after launching the second missile - to increase probability of engagement of the first target. In such case extrapolation period for the first target takes only couple of seconds (let say 7 -8). But can be delayed somehow. Maximum delay is somehow several seconds before missile should go to semiactive.
Again ts position is somehow extrapolated, so if separation in time is low (couple of seconds), and if target has not changed trajectory significantly - its position is somehow known. Radar searches in that area. Gets lock. Firing solution (precise position and vector of target) is being re-developed. Coordinate system, from launch time - for first missile is restored. Missile gets updates. In final part the first target is being illuminated and missile goes semi-active. The second target is all the time extrapolated, and missile goes using only INS.
8. The system or pilot decides that the first missile finished its work. This can be done by system - after calculated - estimated time. Or by pilot manually, or some combination of them (system estimates time when the first missile should hit the first target - but up to pilot is to decide to switch target). Some hint might be - if target "disappear from lock" or changes its vector speed (value and/or direction), suddenly.
Points 7, 8 takes in minimum a dozen of seconds, lest say - between 12 and 18. All this time - the second target not need to change its flight path significantly.
9. Radar switches to the second target. Postion is estimated. Hopefully regain lock. Rest is known.
This scenario assumes that radar works at single target at time. Position of the second target is extrapolated that time (both in radar and in missile). Significant changes in flight profile, for extrapolated target - may lead procedure to fail. For short extrapolation time - it can even work. But time is shared for both targets - less first target is in extrapolation -time - the more time is the second.
To be honest - chances to hit both target - are only theoretical.
Chance to hit only the first target - reasonable, but lower than if just to work with a just single target.
Chances to hit the second target - well, questionable.
Some optimal, but still possible of being implemented - scenario, is that radar can work with both targets the same time.
And can provide updates to the both missiles
So this would like like above - but some dual target track can be achieved and maintained.
I do not say how this can be implemented : dual track only (DTT) or TWS. But in any case - this should be precise enough to provide corrections for missile(s) for two targets. And I do not think - it out of possibility of Soviet N-001 hardware.
It is rather of developing and testing somehow algorithm (software).
In such case procedure looks similar as above but:
1. There are selected two targets to be engaged. They are being started tracking with precision enough for create targeting solutions for R-27R(E) missiles.
2. First missile(s) to the target is launched.
3. When in flight - it is provided target position update to the missile. Both targets are tracked in parallel.
4. After some time (time separation), when in range, the second missile(s) is being launched. There is no need for some "preparation" as targeting solution is constantly updated and ready for the second missile.
5. Two targets are being tracked. If necessary - updates for missile(s) is provided on channel and code (liter) assigned to that missile that requires it.
6. When the first missile is close to the first target, radar needs to goes to single target track*. Radar just has stayed in position of the first target (no additional search for the first target is needed). It stays for some estimated (computed) time necessary to finish guidance.
Similar as in the previous scenario - return to to the second target may happen manually , automatically, or both.
This time in such scenario the only "blind time" is for the second missile, while illuminating the first one in STT.
In that time position of the second target is approximated both in radar and the second missile(s). This time could take from couple to several dozen seconds
7. System switches to the second target. Searches in extrapolated position. If finds - goes to single track, provides update to the missile and if it is time - starts illumination.
*take note - that I wrote that "radar needs to go single target track", and no : "radar needs to start illumination". If we assume some dual - target track - in such mode - radar constantly switches between positions of two targets, working either on the first or the second. Update of parameters - when antena is pointing target - can be counted in fraction of second - let say 0.2 s (See documents T9 and T12 - you know what I am talking: in tracking - iteration period is 20ms - one for monopulse target tracking and speed tracking, another 20ms - is for distance tracking. So in 0,2 - there are up to 5 such cycles. If we assume illumination additional 30ms is required, so : angle - frequency tracking 20ms / illumination 30ms / distance tracking 20ms / illumination 30ms - so 100ms. In 0,2s - two such cycles , with 4 illumination periods.
Depending on angular positions of targets, switch time can be quite short. Assuming antenna speed 70 deg/s (in reality is more - this is just scanning speed, antenna can move faster - but I do not know how. But in T9/12 when switch to locking - there is said "with maximum speed". But assuming 70 deg , and separation between targets 15 deg - switch time is 0.2 s + some time for positioning, let say total 0.3s. So we can assume from 0.5s cycle time, refresh and so 2Hz rate in DTT mode, and in worst scenario up to 1s / 1Hz. In final part of that mode - radar can illuminate target as well. So radar needs go to pure STT - only about - lest say 5 seconds before impact. That would be more than enough. Maybe 8 in the worst case, if targets are more separated and DTT update rate lower is ~1s.
Another problem is that position of the missile is also not known precisely. It is only estimated - when they should be. Missile flight is just real case - and missile can fly somehow longer than predicted, or earlier. And that imprecision that also should be take in account.
(In ideal world missile should "tell" where it is, and how far is from target. But there is no down-link. If this depends on me - I would check if proximity fuse is working - if it works in the frequency band of radar)
Another problem is when to stop illumination for the first target - and switch to the second.
This should happens when missile finished it work (either hit or miss target).
But -this is not known precisely at fighter.
If pilot or system detects that contact with target is lost, this can be clear sign to stop switch to the second target.
(Here once again - some uplink, or some "hints" from fuze would be more than useful)
But in other case still - some additional seconds are needed, in case that missile still is working.
So this is "blind period" - when the second missile goes INS.
So once again : missile is illuminated in DTT cycle. With high ratio cycle - this can be done to just several seconds (3? 5?) before impact. But as the postion of missile is is not known precisely it is also not known, "when impact time will be". So that need some extra time - for example additionally 4s. So continues uninterrupted illumination would starts 9s before estimated target hit
Next - target can do "unexpected" maneuver. if this is done - in STT phase - there is no other option like extend STT phase.
Finally, pilot/system does not know, when to stop illumination and switch to the second target. If contact with target is sudently braken - this can happened quite immediatly. In other case - some extra time is necessary (still 4,5 seconds, after).
And that is all "blind" time for the second missile. It can be as short as 5s - if we system knows where own missile is (but it does not...), and hit was "detected". Or as long as 15 seconds if we take in account all "unknowns". Or more if target did forced maneuver extending STT time. Uhh..Really complicated... even in theory...
When the first missile hit target, or better - when we stop working on the first target, the second missile should be in such distance that - it is still before terminal guidance. So before it goes semi active. But we have to add - additional time - for radar to re-find and re-lock to the second target, and if possible - provide corrections.
Separation time necessary is expected time when the second missile goes blind + some estimated time to regain lock, and provides updates to the second missile - and that needs to be accomplished before second missile goes semiactive.
Estimated time of regaining lock - depends on how long extrapolation time was.
For 5 seconds of (INS/blind), and dual lock, regaining of lock can be immediate: so as low as 1 to max 2 seconds.
For some most possible case - when - missile extrapolation took 8-10 seconds. - this can take from 2... 4, 5 seconds if some small search was needed.
In the worst case - when INS period was some dozens seconds - well, if the second target not was flown strictly straight, it can be anywhere, and regaining lock may be impossible. Also missile flown in wrong direction for long time ... so is in wrong place...
Corrections take 1/3 s (as I remember).
And then we must count time - for illumination of the second missile.
If time of STT for the first missile is the same as for ilumination time (both in STT or in DTT) for the second - we can just skip this.
But illumination for second missile has to start earlier (not just in final STT, "3 or 5 sec").
Assuming missile flight time 30s (up to 60, 70 is in total - but this is for max range that is somehow unrealistic, unrealistic to fire missile on the longest range) - and that up to 70% can be inertial - it is wise to assume at least 10 s for illumination time. Or slightly more 12-15s, So this illumination takes from 5 till 7 seconds more than just STT in the first case. Let assume 7 s more.
cut some calculations, to be honest - it is not so easy to calculate

, lets try:
optimistic case : 5s for "blind time", 1 sec for regaining lock, and then 10s for second misisle to be iluminated - means - separation time should be at least 16s
In some more balanced case: it is 20s "blind time".
( when missile position is not known: 4s need to be added "in advance" (for this imprecise missile positon) to those standard 5, and 4 after "extra time" ("do we hit target?") Also if there is some small maneuver after radar goes STT - some additonal 4 s added - so this can take up to 20s..)
+ time for regaing lock - this should take as long as 4s
+ and 7s for accounting that second missile should be iluminated longer.
So all in all this is up to 30s of separattion time. And this is not the worst case.
So, we see that - this can work, but also can not work at all. Depending on case and luck. Pilot should take separation time at lest 20s, still taking possibility that second missile can not work.
He should select the closest target from enemy formation as first - and fire at them relatively long range (but not maximal!) with R-27RE. The second target should be the last one from formation. And to be targeted -by closer range R-27R. This should provide separation time at least 20s or more. At least in theory. In reality, with complex tactical environment etc - well... maybe just better to get single target and launch missiles from different ranges to them
To be honest - it does not look convincing. If one can use some feedback from missile (like detection of fuse missile "knows" exactly distance to target and closure speed when close to target - proximity fuse should start. That would be information that radar should go to STT. And proximity fuse will not work if missile hit target. Or it can stop - if missile miss (that why it is called missile

). In such cases - blind time may be as short as 3...5 s. Regaining lock with the second target would be almost instant. But still separation time - should take in account some "delay of missile in flight" or that target just turn -still complicated.
In another "fictional scenario" - if we assume high rate (2Hz or 1Hz) dual target track - and if it is possible that in "the the last meters" (closer than 3km before impact) the main beam can be supplemented with some "flood array" just to fill the gaps (in this 1Hz or 2Hz cycle), then there would be no "blind period".
Or, when illuminating target some imbalanced DTT approach may be used: cycle like 2s for tracking illuminating the first target and just 0.3 - 0.5s - to snap to to the second target - to just update position of second target. And sure -this "0.5"s pause - still may be problematic.. so for short period of time, , when missile is expected to hit target - antenna may stay at the first target. Let say for 5s. And then return to unbalance again for couple of seconds (just for case the missile for the first target is "late")
But this is just pure fiction.
Let assume other scenario, also
somehow SF, fairy tail, but maybe still possible... - when Su-27 is not alone , but in formation. And some of planes (one or more) are "active" - and shot missile and at least one (leader?) is not actively - but just to keep tracking and providing information to active one.
In such scenario to make sense - at least 2 (or more) planes are "active" and target up to 4 targets and one. One is passive - not launching (initially) missile .
(BTW in 2 fighter formation - this have no sense - as 2 plane can engage 2 targets in normal mode).
We assume that they are connected with datalink (TKS-2) and its position is somehow relatively aligned each other but not perfect.
(Alignment - is done - by comparing trajectories of targets -both in active fighters and passive - just to match them and correct possible errorS translation and rotation - I can provide some citation for that from book**)
What can this bring benefits?
First - during "INS blind time" of second missile - position of the second target is not just puerly estimated - but is known - with some error but is known. If the second target take forced maneuver, still active fighter can update missile. Also regaing lock, even after long INS time - could be relative fast, and possible.
Now the whole scenario may be possible even in case of force maneuvers of targets.
And if in such scenario : fighters in formation can share "targeting data" , "passive" fighter - when necessary - can illuminate one target when this would be required. This can happen when - for some reasons - the second missile can not be illuminated in time by own fighter. The "passive" fighter then can "save" that missile(s) providing illumination.
If such "sharing targeting data" is possible, other scenario may be possible:
In two (or more) fighter scenario, when engaging one (or multiple) target(s), one fighter can take role of "shooter", other(s) role of "illuminators". Shooter would take high speed, high altitude- to provide maximum energy from own missiles. He will, leave "iluminator(s)" behind 10 or more km, can close to single or multiple targets , and from close range - non escape zone - he would launch own missile R-27R(E) - especially that energetic one to target(s).
Sure - he will be targeted by Aim-7 missiles from enemy. But Aim-7 has long range due to boost sustained profile - but not so high speed. In topic for Skyflash - there are provided its range, (in long pdf) for Aim-7F (but M share the same engine), for maneuvering and non-maneuvering case. And guess what , for non-maneuvering - range could be as high as 40km ir more (Fighter and target 1,5Ma, high altitude) but maneuvering (rotation with assumption 4g) it drops to as low as 10-12 km (I am writing from memory, one can check).
So shooter - takes shoots - with R-27RE close (but not too close

). Missile(s) launched relatively close, from high speed fighter, have high energy and high chance of hitting target.
And shooter takes rapid turn, high g, goes in the dense atmosphere... and start escaping to those Aim-7. He did his job, and now his job is just to survive.
And now - "iluminators" takes own role. Each "iluminator" illuminate just single target, from long distance. Iluminator(s) is(are) in safe distance. And they did own job out of range Aim-7 missiles.
Additionally they can fire own missile, especially if target(s) survive the first attack.
Additionally - if they are more targets behind. Then they can work "in dual target mode".
The first target is being targeted for the missile from "shooter". "iIumminator" has still much time to launch missile(s) to the second target - so time separation is high. And can happened that "illuminatior" fires missile after the first missile (from "shooter") - hit target, but still having ready firing solution for the second target (dual track). But may happen that the second missile is being launched slightly before the first missile from "shooter" gets own target.