Hmm. That's because, at the moment, I'm confined in what I write by the source material available to me. Beforehand, with all the French and Indonesian material, I had the whole of the Maughan Library to plunder. During the summer holidays, I'm stuck at home. This doesn't mean I completely lack sources; it's just that I'm overwhelmed by the ubiquity of actors biographies and works on international relations.
I rely a lot on JSTOR, but so far I haven't seen anything on there that'll adequately (and in a simple fashion) introduce a layman to space travel in the early 1960s. I have had consultation with another member who had the kindness to PM me out of the blue, but that's as far as I've gotten, because realistically I'll only be able to concentrate on space travel in October.
JSTOR probably isn't the best source for space history in the first place, anyways. The
NASA History website is a really excellent resource for that sort of thing, and totally and completely free. It's got a number of full-length history books available as PDFs or online. Obviously, it's NASA-only, though.
Could you possibly give me a just-as-detailed description of Soviet space ambitions (in terms of specific models of rocket, goals etc)? That would help enormously.
The problem is your removal of Khrushchev, which really mucks things up enormously. The Soviet human spaceflight program had no really specific goal until rather later, instead being driven by the whims, more or less, of the General Secretary. Even later it was more or less reactionary to the US program almost up to the end of the Union itself (witness Buran).
The biggest thing to recognize about the Soviet program, as opposed to the US program, is that it was not a centrally-managed organization that had a goal and was reaching for it. Instead, it was a viper's nest of intrigue and overlapping fiefdoms where each design bureau head usually had his own ideas about what the program should be doing, especially the top three: Korolev (head of OKB-1), Glushko (head of OKB-456, and later OKB-1), and Chelomei (head of OKB-52). This led to constant infighting that seriously crippled the Soviet program. Probably the most prominent example of this infighting is the refusal by Glushko to build the large cryogenic (meaning kerosense/liquid oxygen) engines needed for Korolev's N1, forcing the latter to employ a different, much less experienced design bureau. That took place before the POD, too.
Chelomei, in particular, was a relative newcomer to the whole space scene, and was relying on the patronage of Khrushchev to break into it. He even went so far as to employ his son, Sergei as an engineer. With the earlier and more violent fall of Khrushchev from power, I imagine Chelomei is left in a difficult position. Most likely, as IOTL, he gets marginalized after this, although not completely removed from the space program. One significant effect this might have is effectively killing his UR-500 rocket, which had just started development. It's better known as the Proton, and since the mid 1960s has been the medium-lift workhorse of the Soviet and later Russian space programs. What might take its place would be a downrated version of the N1 which (while having a deserved reputation for problems) would likely do a bit better ITTL, where there is no race pressure or anything of that sort. It does depend a bit on whether or not Mishin is Korolev's successor though. And yes, there will be a successor; Korolev's operating table death was only a proxy for massively metastized colon cancer, among other health problems. It's very unlikely that he could have survived much past 1966 or 1967 in any case.
So, all that left aside, what will the Soviet space program look like? Most likely, much like and yet unlike the historical one. I expect that the Vostok program will continue, in the near term, for a few more flights to demonstrate certain capabilities (rendezvous, for example), but will not be followed by the Voskhod program (which was pure propaganda). Instead, like the Americans, there will be a gap until 1966 or 1967 when the first of their definitive spacecraft, in this case the Soyuz (probably), will fly. Like the Americans, this will demonstrate all the important things that couldn't be demonstrated by Vostok (and speaking of the Americans, the Mercury program is likely to drag on a bit longer than it actually did with a series of 1-3 day duration flights in late 1962 and early 1963.). That means they'll probably rely on R-7s (another Korolev product) throughout the program. Sometime around 1970 or so, the N1 is likely to have its first failure, but if they do get it to work it would probably end up being as vital to the Soviet program as the Saturn C-2/C-3 will likely be to the American program.
And, of course, to get off the theme of rockets and capsules, you should probably take into account the robotics programs, such as planetary exploration, spy satellites, communications satellites, weather satellites, and so forth. For spy satellites, Dwayne Day's articles in
The Space Review are an excellent starting point (and, for the purposes of TTL, probably more than enough). For civilian satellites, the '60s were an important time, when most of them were first flying. The first weather satellite was actually launched in 1960, and they were followed up at a high rate. It's about the right time for space-based hurricane tracking and the like to start, IOW.
Robotic exploration, like the Soviet program, is probably going to look quite similar yet dramatically different ITTL. Most of the differences will probably be in the lunar exploration program, which was heavily warped IOTL to service Apollo. Without those pressures, the Ranger program is probably longer and more elaborate; among other things, JPL wanted to hard-land a small capsule of instruments on the Moon in later flights, which might actually happen here. The Surveyor and Lunar Orbiter programs, furthermore, might not even exist as such. A Surveyor-like program is likely, but Lunar Orbiter might be replaced by or or more lunar orbit missions (akin to Apollo 8) that fly some type of mapping equipment to the Moon (there were plans to do so IOTL, should the Lunar Orbiter imagery prove inadequate). Similarly, instead of leaving Venus to the Russians, ITTL we might dispatch landers and orbiters to the planet starting in the late 1960s. Most of the difference will probably come in somewhat more abundant funding compared to the human program, without the pressures imposed by Apollo IOTL.