You're right about the sleep schedule, although I have to admit some people are more creative/productive at night, while others during the wee hours of the morning. In Gretchen Rubin's Better Than Before, she talked about the Lark vs the Owl.
Pros and cons.
I have similar issues like you too, because sometimes when I get excited with a new idea or concept, I'll stay up and work on it. Sometimes it works out well, but like you say, after a while, I'm just staying up for the sake of staying up. :(
One thing that works, though, is to sleep in cycles of 90 minutes. So sleep either 1.5 hours, 3, 4.5, 6, or 7.5 hours. You will wake up in the right state of mind. Try it.