Has he shown any of the following symptoms?
Nightmares or night terrors
Bedwetting
Snoring
Restless Leg
Reason for asking is that I suffered with these as a child, starting around his age.
If some of those, you may find he has a lack of regular circadian sleep (not as scary as it sounds) If all is a possibility, I would mention to his doctors.
If your attempts to help him (which are very good, btw) seem to start out okay, but stop working over time, they may order a sleep study and that is a Very good thing.
I know this sounds even more worrisome, but I can say from experience that finding these things out early in his life will be beneficial to him AND you.
Sorry for the long post