When you BF in the night, is he just sucking for a little while to go back to sleep or is he really drinking? It might be worth an experiment where you actually do a "day" feed in the middle of the night - both get up, wake him up as much as is needed to get him really eating, change his nappy, give him the other boob, do whatever you can to stuff him as full of milk as possible - and hope that he lasts for longer. And maybe try a sleeping bag rather than the wrap if you want to put him in his cot - they make it harder for wriggly babes to get to the end to bang heads.

hugs and hoping that something makes an improvement
Kate