I figure that at least some of the U.S. government/bourgeoisie would surrender, at least enough to spare their own lives

Amerikkkan imperialists must have a degree of self-preservation to not want to risk the entire globe when they could scatter away and fight later

There's no excuse for this level of wishful thinking about global nuclear war. The United States is not going to launch a limited nuclear strike against another nuclear power and then surrender in the hopes that its leadership will be left alive. Nobody on earth would accept a surrender that left those people alive after a nuclear first strike. If the US launches on another nuclear power, the US only survives by completely obliterating every other non-occupied nuclear power before they have a chance to respond. If the US does a nuclear first strike without completely disabling any potential response, every other non-occupied nuclear power in the world would be obligated to immediately unload everything they have on the US. To do anything less would leave a country with no credible deterrent to US attack, and the US would be obligated to exploit that vulnerability to eliminate the threat to its hegemony. A nuclear exchange will either end in the total destruction of the United States, or total US world domination. Either option means uncountable dead and complete global economic and environmental collapse no matter who rules the wasteland. For average people that amounts to quick death or slow death. An improvement in anybody's current living conditions would not be in the cards.

The personal sense of self-preservation in individual members of the national bourgeoisie or congressional middle men doesn't matter at all if one senile dipshit with one foot in the grave pushes the button. It doesn't even matter what a majority of the US ruling class thinks if a few true believers in the right positions with enough hubris and self-delusion decide to gamble that the benefits of winning outweigh the likelihood of retaliation. It's all or nothing once the first nuke flies. There can be no reconsideration or negotiation after that threshold is crossed. It's either live by killing the enemy completely, or die taking them with you.