You need a crate or a bell. Either crate him at night, or put a bell by the door so he can at least wake you up. Loki rings his bell if he needs to go out at night. Sammy bites my nose and dances on my head until I wake up...
When Loki was a puppy we crated him at night because he would whimper when he needed to go out. I still think you have a combination of him drinking too much too late and him not being able to tell you he needs to go out.
Also, mine are housetrained but they have to go so bad in the morning that I let them out *immediately* when we wake up for they will go on the floor by the door. I've found that one last trip super late at night (like 11-12) helps them sleep an extra hour or so in the morning.