Here are my observations after a playthrough of the sandbox game.
Prestige is quite generous. I was usually one budget ahead, ie had more than achieved the top prestige in each period. And this was with a slow pace of advancement, I didn't achieve a Gemini Direct Ascent moon landing until 1984. Are the prestige awards less generous in the other campaigns? I was awash in cash. Am I meant to be saving up for a manned Pluto landing in the 2090s?
Some of the programmes could be folded into each-other, or else some more need to be split up. The Gemini Direct Ascent programme includes Lunar Flyby and Lunar Orbital, so when it comes to Lunar Probes, why are Lunar Flyby and Lunar Orbital different programmes? There should be some consistency here. Because of this the "max different programmes" of HQ would of course change; if programmes are split we need as many as in the game, if programmes are merged this max number could drop, for example if all the lunar probes were one programme, and all the venus one, all the mars one - we wouldn't need 10 slots in HQ.
It would be good if the system kept track of and displayed the number of missions, both successful and failed, that a particular mission controller or astronaut had been involved in. From my first manned suborbital flight to Gemini landing on the moon, probably half the missions were done by two astronauts, and almost all by 6 or so. It was not surprising that some of them started quitting while the 57yo veteran of a dozen manned missions stayed on happily from 1959 and ended up walking on the moon in 1983

If on their roster sheet we had a "missions - succeeded/total" that'd help.
Further on astronaut experience, just as equipment reliability improves after missions, so too should astronaut skills. If you've actually done an EVA your EVA skill should improve, yes? This ties into the above, in that if putting them in space improves their skills, we have a reason to use more than the 2-3 best astronauts all the time.
I understand you are still looking at giving people choices of what equipment to use for missions, or at least boosters? I was a bit confused when I did a Mariner orbital mission to Venus and already had the Saturn V pushing big Gemini into space, then when I wanted to do a Venera lander needed a different (Proton) booster starting at 5% reliability.
Overall it looks very good.