Have you considered a polyphasic sleep schedule? If you truly do have a non-standard circadian rhythm, you should be able to adapt one of the dual core schedules towards it.
Maybe? I was thinking more that stuff comes up that affects my schedule, and I don't be forced into living with the constraints of a 10 p.m. bedtime (or whatever time I set). More to the point, I am more disciplined about getting to bed before 12 a.m. I do not want to go bed at a fixed time.