Our little guy is in bed by 8:30-9:00, and is up by 7:00-7:30.  Sometimes he can be coaxed to sleep until 8:00, but very rarely!  He’s had this schedule since he was about 2 months old (lucky us!).  I’ve heard that some kids begin to sleep less when they are on a higher dose of Cortef than they need, or being too sleepy if they’re not on enough, but where you seem to have each problem at a different time, I wonder if it’s more of a sleep issue.  Have you tried a bedtime routine?  Ours has been snack, bath/toothbrushing, story/song/prayer, and then bed since he was an infant, and he seems to have done really well with this.

Good luck -