I have a neurotic puppy myself and this all sounds pretty normal. He's a puppy!! Cut him some slack He's definitely not trying to gain dominance over you. A puppy this young and well trained (from what you've told us) should know its place in the pack. Every time that he paws or mouths at you, you said he gets more excitable every time you try to stop him. I'm going to assume you probably push him away or give him a "No!". Even though it doesn't seem like it, you're giving him attention/rewarding him for his behavior. In our eyes, it may not be positive or good attention, but it's attention nonetheless.

First thing is first, a tired puppy is a good puppy! I know he's young, so don't take him for a marathon or anything. A simple game of fetch can tire a pup out for a good 3-4 hours. Intermittent games will keep your pup healthy and tired and our of your way. Second, are you absolutely consistent with training? I was going to suggest getting up and walking away from the pup every time he mouths you. Walk into an entirely different room and don't allow him to follow you. He's doing all these behaviors for your attention. So if you ignore him 10 times and give attention even once, his bad behavior will continue. You have to stay absolutely consistent and firm. Be warned, though, your pup may go through an extinction burst, so things might get worse before they get better. Hope that helps!

(Also, don't alpha roll your pup. It's completely outdated and has no positive effect on the dog whatsoever.)