Found why Sims won't stay asleep (in my game)
I'm posting just in case anyone else has this issue.
Shimrod's apparently fallen off the face of the earth, unfortunately, as he's one of my favorite mod creators. However, I understand life has stuff going on, so I hope he'll pop back up at some point.
Anyway, my sims wouldn't stay asleep. They'd go to bed only to pop back up a few seconds later. Removing mods is my last resort, because I download a lot. Luckily I put them all in folders to make it a bit easier.
I did everything I read to try. Resetting sims, resetting beds, replacing beds, repairing the game. Nothing worked. So I started narrowing down the problem mod.
It's Shimrod's Share Beds with Everyone mod.
So if anyone else has tried everything for the same problem, and has his mods installed, check if you have this one.