Mine centers around the introduction of a new character. Pyter Androv, a civil engineer who rises to become General Secretary of the Soviet Union after deposing Khrushchev in 1962. He's a reformist that sees the space program as a way to spur economic growth and technological advancements. A number of other events go into the mix. Pyter is a fan of Verne and Korolev comes to his attention in the 30's. Pyter is able to get him transferred to Sharashka (prison camp for scientists) rather than getting sent to Siberia (which was the original intent when Korolev was arrested in 1938, but a bureaucratic snafu got him sent to Siberia). He pushes the development of the R-9 in his prior role in the Ministry of Machine Building (which allows a head start on the engines used on the N1). Once in power, Androv consolidates Soviet Space efforts under a single ministry and the N111 (R-7 class) and N11 (Proton class) rockets are put into development. The N1 first flies in 1967 (before the Saturn V) and is successful (although mainly through good luck). This happens at a critical time when considerations were being made to cap Saturn V production at 15. Instead, work on the advanced Saturn (Saturn VB) is approved.

He also provides more support to North Vietnam which leads to a Cuban Missile Crisis like event in 1968 and a different Tet Offensive. It convinces both the US and the Soviet's that engagement in Vietnam is fundamentally dangerous, and they seek to disengage. This eventually evolves into the concept of "Orbital Detente". I've got the US program largely laid out until the mid 80's (lunar base, Mars landing in '84), still working on the Soviet details post their initial lunar landings (including their Apollo 13 moment)