Actually, you can try a coup, but it cannot succeed, because coups agains faction leaders never do.
Also the party support is irrelevant because couping isn't an option and there are no elections in the USSR that could get a democratic party in power.
The options I see are executing an install democracy wargoal against the USSR (of whom I have heard rumours about not always working as designed) and modding either the savegame or the country starting file.
Doing so will most likely break down the entire event chain for the USSR, (and from Summer '39 onward also affect Germany), for some events require Stalin to be in power, and I guess it is a reasonable assumption that Stalin wouldn't be part of a democratic government.
About fascist USA, the differences would be much smaller, USA is too neutral to do anything before Japan attacks, and since Japan is usually a member of the Axis, they'd join the Allies anyway (or the Comintern if the Allies have lost a lot and the Axis is at war with the USSR already). Fascist USA might be stronger than usual due to mixxed industry, though.