Therefore, to get 5 extra Skylab missions as NOMISYRRUC suggested another 2 Saturn IBs would be needed and CSMs for them.
For What It's Worth
Part Two
Yes indeed. To recap.
12 Saturn IB and 15 Saturn V were initially built. Circa 1967 NASA tried to order another 18 Saturn IBs and another 10 Saturn Vs for totals of 30 and 25 respectively. NASA got permission to order 2 of each, which were cancelled a year or two later, so all that was completed were the first stages of the 2 Saturn IBs (SA-213 and SA-214).
I think that at the very least Congress would have given NASA the money to finish the launchers ordered circa 1967 if there was no Vietnam War. So, a minimum of 14 flight rated Saturn IBs and 17 flight rated Saturn Vs were completed ITTL. Therefore, there was no need to cancel Apollo 20 when Skylab was upgraded from a Wet Workshop to a Dry Workshop.
5 of the 14 Saturn IBs built ITTL were launched 1966-68 leaving 9 available for AAP/Skylab. That's enough for 8 regular visits to Skylab and one on standby for the Skylab Rescue mission. If there was no Skylab Rescue mission ITTL its Apollo CSM and Saturn IB would be used to perform the ASTP mission ITTL. If there was a Skylab Rescue mission ITTL the final Skylab mission would be cancelled to provide the necessary hardware. That is unless the final Skylab mission was the one that failed in which case ASTP would be cancelled because there wasn't the hardware to do it.
All other things being equal Skylab is launched in May 1973 but it's launched by SA-516 instead of SA-513. Does using a different launcher prevent the OTL accident? Don't know. Does using a different launcher result in a more serious accident? Don't know either. So I'm presuming that it's the same as IOTL.
Skylab 2 is still launched in May 1973 and is still of 28 days duration. Skylab 3 is still launched in July 1973 and is still of 59 days duration. Skylab 4 is still launched in November 1973 and is still of 84 days duration. And that is where things change.
The 5 extra missions were named Skylab 5 to Skylab 9. They were launched at intervals of 3 months from February 1974 to February 1975.
Skylab 4 to Skylab 9 overlapped and the space station was continuously occupied for 18 months from November 1973 to May 1975. The overlapping of Skylab 4 to Skylab 9 also meant that 6 astronauts were aboard the space station for short periods. Each of these 6 missions delivered a Resupply Module (RM) to Skylab, which was launched with its Apollo CSM and docked to one of the 5 docking ports that it had ITTL. (See footnotes.)
However, all other things were not equal. Not cancelling SA-516 and SA-517 circa 1968 probably means that the decision to make Skylab a dry workshop is made in 1968 rather than 1970. Also Skylab may be launched a year or two sooner with Skylab 9 splashing down in May 1974 or May 1973. Or more (or all) of the 18 Saturn IBs requested circa 1967 are built and there can be as many as 24 CSM flights to Skylab instead of 3 with the possibility of having it continuously occupied for 66 months (5½ years).
Which long-windedly brings us to the supply of Apollo CSMs. We need a minimum of 9 for the
"at the very least" programme and 25 if all 18 extra Saturn IBs are built. We've go 4 flight rated Block II Apollo CSMs (116 to 119). We don't have CSM-111 ITTL (which was used for the ASTP IOTL) because its used for Apollo 15.
There is also CSM-102 which was used to checkout Launch Complex 34 and CSM-105 which was used for acoustic tests. AFAIK the plan was to make them flight rated CSMs after the tests were completed and that said plan was not carried out due to budget cuts. ITTL the budget cuts are less severe so they may be rebuilt as flight rated CSMs, which brings the total to 6 when we need a minimum of 9.
According to the Wikipedia article on the Apollo CSM a total of 3 non-flight rated Block II CSMs were built with the designations CSM-098, 099 and 100. Maybe NASA can
"do a Challenger" on them hand have them rebuilt as flight-rated CSMs in the same way that they had the Space Shuttle structural test article STA-099 rebuilt into the flight rated OV-099 Challenger. And if they can't or if it's cheaper, they order some brand new Apollo CSMs from Rockwell.
Footnotes
1. Since I wrote my original message I've come around to
@Rule of cool's suggestion that the Apollo CSM's orbital rating would have been increased from 90 days to at least 120 days, because (as he wrote) it would make the above easier.
2. The Multiple Docking Adapter (MDA) on the OTL Skylab had 2 docking ports but only one was used. The MDA on TTL's Skylab had 5 docking ports. I'd like it to have a sixth docking port at the rear as well. I don't know if that was technically feasible, but there would be enough money to do it ITTL if it was.
3. Follow this link to Astronautix.com for more details on the Resupply Module.
http://www.astronautix.com/a/apollorm.html