I started taking melatonin last night. I think it's working. About ten minutes after I took it, I started to become sort of drowsy, and it didn't seem to take as long to fall asleep as I'm used to. Then, at 7:00 this morning, I awoke of my own accord, well-rested. But, it was too early to get up, so I went back to sleep, and then I awoke a little later from the alarm, cranky.
I read that it takes a few days for it to come into full effect. So, we'll see if this helps to improve my sleep cycle a bit.