That’s where the melatonin could help—it can keep you asleep longer. There is even a 10 mg time release version that will do a number on you.
I’ve been using melatonin for about a year. My doc suggested it. Doesn’t seem to do much for me. I read a study recently that says it helps you get to sleep a few minutes faster and stay asleep a few minutes longer, but no huge improvement. That’s consistent with my experience.