Yes, I like your thinking. So we're looking at America, Ottomans, Russia or Sweden. I don't mind any of those.
They're all going to be quite decent, but America will give us the best start.
We can maybe reduce the number of turns later if need be, but not much will need to happen for the first round of turns. So maybe 20 to begin with, then 15 after NC then 10 after T130ish (when the renaissance units come online). When we get stuck into long wars, we will have to make detailed notes of where the troops moved - e.g. "That minuteman got smashed and has 1HP, just to let you know".
I know you liked the idea of Random civ, and I don't mind that in general, but I really like wide violent culture and domination so we should definitely pick.