I think the training theory is crap but you already know that! LOL
In my opinion, putting him in a heel and then correcting him is going to confuse him. He has no idea what he's being corrected for. Like my trainer said, dogs have a 3-5 second recall on connecting things. So, he breaks his stay, he gets put in a heel (which is allowing him to get away with breaking his stay) and then he gets corrected. First, I think to much time has passed so he doesn't have a clue why he just got a pinch. Second, he's being corrected for being in a heel.
In my opinion, he should have been put back in a sit (calmly and without correction because even with 4 classes it's still kind of new to him) and just start over. Reward him for staying in the sit, put him back with just a verbal (negative) marker if he breaks.
btw...I really, really, really wish you were closer so we could train together!