Ok, here are a couple more pointers to help.
You said he would sniff your hand and then bite? I think I would try and catch him, before he bites. So if he comes up and sniffs, maybe tell him a good, and give him cookies, before he bites. The goal with training a puppy isnt always to correct bad behavior, as much as teaching them good behavior and trying to set them up for success. I might take a step back and teach him that nose or tongue on skin means cookie and teeth means mom stands up, walks away, and pays no attention to you. Then once he is a little more gentle, start working on "off."
Also keep your sessions very short, like maybe 5 mins, several times a day. If he has obviously gotten to bored or stressed by the exercise, then you worked him to long. I cant remember where but I heard a great analogy for working with your dog:
Think about if you went to a friends house and were playing a video game. Your significant other comes in and says its time to go, but you still want to play the game. When you return to your friends house, you will probably be excited to play that game, again. If, on the other hand, a friend forced you to play the game for much longer then you wanted, you might not be as excited to go back to the game, again. Its the same with our dogs. We want to make our sessions long enough for them to progress, but always short enough that we leave them wanting more. this way they are excited to come back to it and keep learning. this time frame is different for every dog so you will just have to watch his body language and get a feel for what he needs.
There is also something to be said for naming and rewarding a behavior. It is thought that by naming and rewarding a behavior it is more likely to happen, again. You might want to put a word like, Gentle, kisses, sniff, ect.. to the behavior when he does something nice with his mouth. And remember to reward when he is good. Even if you arent actively working with him at the time, if he greets you with an appropriate mouth behavior, make sure to mark that and reward it. Since he doesnt really know what to do, besides bite you, its good to teach him what he should be doing, in addition to correcting the bad. This way he doesnt have to try and guess what you want.
I hope I have helped some ( I really feel for you, it certainly can be frustrating), and I would ask your trainer about it in your next puppy class. Since he/she has seen your kiddo in action they may be able to help with more specific comments.