The bigger issue is that I don't really see the point.
Same feeling.
after a set amount of time (I'm thinking between 20 and 60 hours) (...)
A normal game lasts between 10 and 15 hours, sometimes less than 10. Even your low end bracket of 20 hours is pretty long for a game. The higher achievement is 36 hours, a duration that the devs found abnormal enough to be the higher end of the spectrum.
Just try auto-AIP at Red.Queen level: 1 every 5 minutes. The "default" setup is 1 every 30 minutes, wich is the worth of one planet capture (20 AIP) after 10 hours of play, which is rather few: after 10 hours of play at this difficulty, it's like if you destroyed a planet without taking it (not having some metal, 150,000 energy and 3,000 knowledge). With madder auto-AIP, it's like you waste more than one planet every pair of hours. After 10 hours of Red.Queen game, it's like you wasted 6 planets; the half of a low AIP empire. And you can set auto-AIP much higher.
And this is only speaking of auto-AIP. There is many other ways to augment the pressure on the player(s). Plots like hybrid or preemption, raw AI difficulty, etc.
More specifically on your idea: try the showdown ending.
This is a longer answer than Imago's one, but
in fine the comment remains the same.