Possibly building on Overseer's idea is to have 2 UUs per civ, but not have both or possible either be able to trigger a golden age. So keep the original and just add one to each.
GOTM78 = America - looks like you got your wish!
I liked COTM48 where we had a large island to ourselves, but had plenty of barbies to deal with. Not something you'd see in a regular game. As a sort of inverted variant, how about we start out on a very cramped island/continent with all the other tribes but one. The last tribe lives on a very, very faraway island/continent (this way no one wins too early by conquest). Much of the world lies on islands we have to find and settle on.
Or maybe a game where we have a small to mid-sized island, and all the other tribes lay on an island/continent far/far away that we really can't reach until Navigation. Of course that sort of implies that we'd play on Emperor or below, since we'd have to do tons of reserach ourselves.
What about a say a Deity game of the month where we have the same build rate as the AIs at 60%, but no extra units? Or a demi-god one where we have a 70% build rate, but again no extra units?
What about a say a Deity game of the month where we have the same build rate as the AIs at 60%, but no extra units? Or a demi-god one where we have a 70% build rate, but again no extra units?