I've heard people say the barking collars actually made their dogs worse.
Maybe it's time to change tactics on the barking inhibition since he's learned to associate being behind a closed door and away from you with punishement. He's thinking he's being punished now when you go away and close the door behind you. Sometimes we have to think up different ways to deal with behaviour modification.
When he bites, try just ignoring him. Just refuse to acknowledge him until he stops. And when you leave for school, or anywhere for that matter, have a special toy - like the ubiquitious stuffed Kong or a puzzle ball - that he really likes all ready to give to him. Get him started playing with it, then just go on without making a big fuss. It would probably be a good idea to have at least three different toys that you alternate so that he doesn't associate one toy with being left behind.
Anyone else have any ideas that might help?