The period I really like for NASA alt-histories is the 1969-1972 era. There are plenties of potential whatifs to play with. Early 1969 there were essentially three point of view- Nixon- Townes- PaineCombined, they result in some wide scenarios - The push for Mars or- continuing Apollo or- the retreat to low Earth orbitor- nothing (!) no manned spaceflight after Apollo and 1972. Each four option has its own NASA budget level. Push for Mars: around $10 billion. More lunar exploration: keep the Saturn V production line opened: probably above 4-5 $ billion Retreat to LEO: space station AND space shuttle OR only one out of two. Can be done for $4 to $2.5 billion dollars. Nothing: with a budget of only $1.5 billion, well, there's no HSF after apollo end in 1973. I'm mostly interested in the "retreat to LEO" alt-histories. Some potential scenarios are- space shuttle first, space station deferred (as happened in our days). Freedom- Alpha-ISS history can be modified, for example in June 1993 when Alpha survived by only one voice (215-216 !) - space shuttle first, space station deferred, Skylab A or B as an interim space station - space station first, no space shuttle (Big Gemini and Titan III instead).
That (5-6 Glushko engines) sounds pretty plausible, assuming they're RD-170-ish quad chambered. There is no way they had the time or money to hand-tune a single chamber's combustion instabilities out, as was needed to be done by Rocketdyne with F-1. Even still, they probably still would end up with an N-1 class launcher, which means the lunar system wouldn't be any more complex/less scary than the LOK/LK combo...
The problem I found is that the political circumstances, which led to the large NASA budgets in the mid 60's, had largely evaporated. Unless something substantial occurs there is little political will to fund an expansive space program. By 1967 the Soviet program was in serious trouble and the administration knew it. The congressional class of '68 was more concerned with social programs and "problems here on Earth".Unless something significant happens (say a major meteorite impact in the Indian Ocean triggering a disaster on the scale of the 2004 Boxing Day Tsunami) its going to be hard to swing for a major budget increase. Likewise a much smaller NASA budget was unlikely as well, Nixon didn't want to wear the mantle of "cancelling the space program" and more importantly all of the jobs that went with itBy 1970 you're pretty much locked into a similar funding profile, but there is still lots of fun you can have with that if NASA decides to do something besides the ShuttleKelly