I guess it's nice he wants to be close to you...but it's really not nice that he's not listening to you.
It's pretty basic: you've got a right to get some sleep. All you can do is make it very clear that he's a hard person to sleep in bed with, and make it clear it's not awake-boyfriend causing the problem. It might help to record a video of him sleeping, so that he can see what he's putting you through.
Once he grasps the issue, he might actually want to visit a sleep lab, since it sounds like he's not getting much rest even when he's asleep. Either way, this cannot stand and he needs to get that.
Classic dictionary definitions of clingy and inconsiderate!
(Me thinks this relationship will never move into living together or marriage.)
Yeah...sorry, OP, but unless he ships up, you really should ship him out.