Unfortunately, we weren't smart enough to try one thing at a time. So I don't know exactly what's working, but here's what we've learned about Caleb's sleep issues:
We've been sending him out to play in the sunshine for a couple of hours each day. It's finally warm enough, but he still wears a woobie. So we get sunshine and exercise here.
We've been feeding him beef and meals he will actually EAT every day. So more food, more liquid, and better nutrition here.
Instead of protien before bed (which we give him throughout the day because it works to clear up his thinking, calm his restlessness, and keep him more focused), I've been giving him one or two bowls of cold cereal. It makes getting him into bed a serious chore because it shuts down his brain, so he's too distracted to brush his teeth and can't remember how many times he's gone potty (so he keeps going back again and again). But then his brain can't think clearly enough to keep him awake.
Today we didn't go outside and I fed him chicken. If he still falls asleep, then it really WAS my fault he had insomnia: I was giving him the wrong food before bed.