I'd argue that none of the post-1960s PODs here would work. They might moderate the polarization between the parties, but the polarization would still be the same. None of those PODs are enough to re-shape the polarization.
From the Republican side, as far back as the 1950s, the conservative movement was preaching traditional moral values and economic liberty and anticommunism. Fusionism was an attempt to give philosophical coherence to tendencies that were already finding themselves on the same side of politics. Now you could argue that this was the result of communism: its godlessness and (initially) social radicalism combined with its obvious centralizing and socializing tendencies meant that in a world where communism was a big deal, you were very likely to get a party that combined free market-ism with traditional values-ism with aggressive foreign policy, and consequently the opposite tendencies would also tend to align. That being the case, the earliest realistic PODs are during WWII and its immediate aftermath, to remove the pinkos as a realistic threat.
However, I would argue that the USSR *wasn't* the main reason for this alignment of forces. I would argue that it was the result of the technocratic, regulatory, expert-driven, centralizing rationalist model of the New Deal. The New Deal itself was perfectly acceptable to religious and culturally customary elements, but this model was inevitably going to conflict with using religion and custom as a source of law and practice, which happened during the 1950s. Maybe another way of saying the same thing is that because of the Depression, the United States was moving towards economic regulation and centralism, which inspired a reaction by free market types, at the same time that for other reasons it was also developing looser divorce laws and other trends that inspired a reaction by family values types. In the nature of things, the defenders of one trend were more likely to defend the other and the opponents of one trend were more likely to combine with opponents of the other. So to actually reshuffle the party polarizations, you probably need to go all the way back to the 1930s. You either modify how the New Deal happened and what it was all about, or else you get rid of the Depression altogether and somehow have the US move in a direction of even more economic freedom while loosening mores. As in the 1890s, the result will probably be a a morally conservative economically populist movement.