My three-year-old also wakes up too early, but I can't do much about that except insist that the light stays off until 6 a.m. Writing out sleep rules (not to wake us up too early or in the middle of the night) has helped, but he doesn't get more sleep. He also doesn't nap, so he can't catch up on sleep. So I feel your pain and don't have a great solution.
We do have the rule that bad behavior or excessive tiredness in the evening means an earlier bedtime.
School hasn't helped him sleep any more, but hopefully you'll have more luck.
