Why not try a night without closing the crate door? Shut your bedroom door, close all the closets, make it puppy proof, leave the crate in your room with the door open and see what happens. You may want to leave a small bed on the floor, next to your bed and you can reach down and pet him. Set your alarm to wake up and take him out for a pee in the middle of the night. Probably not the best advice, but I know what its like to be sleep deprived.
When our first dog was about 4 months old, she started doing a similar behavior in her crate, we couldn't sleep either so we let her out and she never peed or bothered us or destroyed anything. It was like she was telling us she was ready to be on her own.
She grew to be a very good dog in every way.