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Wow, very interesting idea. You've made me want to read the time line you mentioned. However, in the scenario you mentioned, the USA will need long-terms issues for the USSR to actually win the Cold War. Otherwise, eventually the Civil Rights movement will succeed and the USA will reorient itself on the Cold War. Even with a more reformed model of communism, the USA will probably have more wealth and GDP. It was a large disparity IOTL, so a lot will be needed to make up for it. It is possible that the Civil rights movement in the USA will align itself with communists?
If that occurs, then the Civil Rights groups could be banned, and the left-right divide in American politics would widen enormously. Since they're communists, the government would treat them as illegal groups that are trying to overthrow the USA, and react accordingly. Since they're pro-Civil Rights, they will have a lot of support and a fairly large liberal base. Groups like the Black Panthers could turn more to terrorism like the Weathermen, widening the split. As more and more terrorism occurs, it would just make the governments reaction more harsh and authoritarian, alienating the USA in the eyes of the world. If the USSR does indeed reform itself somewhat, then Western Europe could look start to question it's allegiance to a seemingly authoritarian country. Then comes the Vietnam war, and all of the international argument which that came with, which finally pushes Western European nations into a non-aligned camp. As the years go by, the only countries like South Korea, South Vietnam and Taiwan, dictatorships propped up by the USA, are American allies, while the other Western democracies shift to a non-aligned camp(I think pro-USSR would be to ASB). Finally, 1989 comes along, and a USA finally fed up on the Civil Rights issue voted a charismatic black communist pacifist named Dr. Martin Luther King Jr into the White house, who promptly ends the Cold War.