I finally talked to my doc -- it wasn't worth making a special appointment, so I waited for my next annual. She said it's not abnormal (though not everyone does) to feel a burst of energy about a half-hour after taking it, as the initial spike of levothyroxine starts to convert. Then it evens out. The tiredness is almost assuredly normal fatigue, now that I have gotten used to "normal" again, and I can push past it if I need to.

She said she thinks there's no problem at all doing whatever I want on 24+ hour events, so long as it mostly averages out. And if I want a boost at 3am, go ahead and take it early, and not to worry about taking it on an empty stomach then.