Good question about the REM sleep! I have no idea, but do know that I don't sleep well at all. After a very busy day when I think I am handling things quite well, I will not sleep at all.
The neuro-pyschologist I saw said that 5 or 6 is good enough...as long as you get the rem sleep!
I think it tends to happen early in the sleep cycle...the first few hours are very important. I have also read many different places that getting to bed earlier than midnight is very important. That is something that is difficult for owls, brain injury or not!
I have tried melatonin....different brands work differently for me. I don't like the groggy feeling the next day, but it certainly is worth a try. Maybe it was someone here or in another context that said you need to take it a few hours before your bedtime.
Good luck!