At present I think that at the very least NASA gets everything it asks for to FY 1967, FY 1968 or even FY 1969. Which means it gets all the money it wants for Apollo, AAP, Surveyor, Lunar Orbiter, the Planetary Program and NERVA to FY 1967, FY 1968 or even FY 1969, including enough money to order 18 extra Saturn IBs and 10 extra Saturn Vs.
Then the cuts begin, but they're between one and 3 years "behind the curve"
I hadn't previously understood this part of your idea, but it makes sense because it's like so many other programmes that start optimistic but encounter financial and politic reality.
To paraphrase Professor Higgins,
"By George, I think he's got it!"
According to the table in Message 197 the peak year in the period we're discussing was FY 1965 the extra money available in the period FY1966-75 is:
- $2,312 million or 6% if FY1966 is the same as 1965 and subsequent cuts are "one year behind the curve".
- $4,328 million or 11% if FY1966 and 1967 are the same as 1965 and subsequent cuts are "two years behind the curve".
- $6,077 million or 16% if FY1966, 1967 and 1968 are the same as 1965 and subsequent cuts are "three years behind the curve".
In the first one NASA gets all the money it requested for AAP in FY 1967 and FY 1968. That includes permission to order 18 Saturn IBs, 10 Saturn Vs and a batch of Block II Apollo CSMs in 1967. The OTL cuts of August 1968 are postponed to August 1969 which results in the cancellation of 14 Saturn IBs, 8 Saturn Vs and most of the CSMs. However, its allowed to complete 4 Saturn IBs and 2 Saturn Vs due to their construction being more advanced and more money being available despite the cuts.
This is why I've written that at the very least SA-213 to 216, SA-516, SA-517 and more Apollo CSMs are completed. It's also why I think at the very least all the completed hardware (including the extra rockets and spacecraft) is used by 1975. So Apollos 18 to 20 aren't cancelled in 1970 and the interval between moon landings might not be increased from 4 to 6 months. The launch of Skylab A is brought forward to 1972 or even 1971 with the number of CSM visits increased from 3 to 10.
If it's the second one NASA gests all the money it requested for AAP in FYs 1967 to 1969. In that case the OTL cuts of August 1968 are postponed to August 1970 so more of the Saturn IBs, Saturn Vs and Apollo CSMs are completed. Therefore, Apollos 18 to 20 aren't cancelled and the interval between moon landings isn't increased from 4 to 6 months. Some or all of the 5 lunar M&SS missions planned for 1969-73 are launched with the number launched depending upon the number of Saturn Vs completed ITTL and whether the GEO "wet" Skylab is launched.
The OTL Apollo 1 fire puts the earth orbit part of AAP back one year. Therefore, the first "wet" Skylab is launched in 1969 and is visited by one ATM and 6 CSMs 1969-70 instead of being launched in 1968 and being visited by one ATM and 6 CSMs 1968-70. All other things being equal the second "wet" Skylab would be launched in 1971 and be visited by one ATM and 4 CSMs 1971-72. Except the "dry" Skylab is still launched in 1971 (as planned in 1966) and it is visited by 12 CSMs 1971-74 instead of being visited by 8 CSMs 1972-74 if the second "wet" Skylab wasn't cancelled. Whether the third "wet" Skylab is launched into GEO ITTL depends upon the number of extra Saturn Vs completed and the number of lunar M&SS missions flown ITTL.
If it's the third one NASA gets all the money it requested for AAP in FYs 1967 to 1970. In that case the cuts of August 1968 are postponed to August 1971 most of the hardware will be complete, the rest will be so far advanced that cancelling them will cost more money and a batch of hardware ordered in 1969 or 1970 would be in progress. Therefore, AAP as planned in 1966 is completed. So 10 moon landing attempts 1969-73 instead of seven 1969-72 including one G, one H, 2 J and 6 Profile-K missions* instead of one G, 3 H and 3 Profile-J missions and 5 lunar Apollo M&SS (Profile-I) missions 1969-73. And 20 Apollo CSM visits to 3 Skylabs 1969-74 consisting of 6 launched 1969-70 to the LEO "wet" Skylab, 2 launched 1970-71 to the GEO "wet" Skylab and 12 launched 1971-74 to the "dry" Skylab.
It would be a similar story for the unmanned lunar and planetary programs, which I haven't worked out in detail. However, in the first one the Voyager Mars probe is cancelled a year later and the Viking missions are launched in 1973 instead of 1975. In the second one the Voyager Mars probe is cancelled two years later but the Viking missions are launched in 1975 due to the lost time. In the third one a pair of Voyager Mars probes are launched in 1973 and a second pair is launched in 1975.
It also means that work on the F-1A, HG-3, J-2S, J-2T, M-1 and NERVA rocket engines continues for another one-to-three years (depending upon the TL) along with the second-generation Saturn IB and Saturn V rockets and more work on reusable S-IB and S-IC stages. If it's the "one year" TL then the result is more money spent for no return. If its "two years" the result is even more money spent for little return and its "three years" the result is a lot more money spent for some return. That is if it's "two years" the S-IC stages from SA-516 onwards may have F-1A engines while the S-IVBs from SA-213 and SA-516 onwards may J-2S engines. If it's "three years" the S-IC and S-IVB will have those improvements and we probably see the reusable S-IB and S-IC stages developed.
Footnote
* There wasn't an Apollo K mission profile IOTL. However, I think the six 14-day lunar visits that were planned for 1971-73 would have been called Apollo K.