(This is exacerbated by the fact that when I'm sleep-deprived, I tend to feel lousy and wanting to doze off through the day, but then in the evening I suddenly start feeling perfectly OK and not wanting to sleep at all.)

I suffer from this as well. It is my totally unsubstantiated theory that this is a stress response. Throughout the whole day your body is tired and telling you to go to sleep, but the Conscious High Command keeps pressing the KEEP-GOING-NO-MATTER-WHAT button until your body decides it must be in a war zone and kicks in with cortisol or adrenaline or whatever.