I realized I forgot to post about how the second class went. It was... better than the first week! Algae still barked upon entering and had a few flare-ups where he lost his brain and had to bark a lot, but by and large he was able to manage distractions.
The big breakthrough in class, though, was that he actually lay down, and moreover did that a few times! I've never seen him willingly lie down in public before. He got a constant stream of treats while he stayed down. Eventually he figured out that he gets rewarded for lying down and kept doing it... which is great!
I also slowed down my delivery of treats during class and was able to keep him pretty engaged and not filled up by the end. He's going through about 8 hot dogs a week, which doesn't seem too bad for when we're doing active training.
During the week leading up to class 3, I've been going through more of the protocol for relaxation with him. He's been having good results so far with staying on his bed even when I walk out of sight through doors and come back. He was put to the test a bit yesterday when I had him wait on his bed while some friends came over. He clearly had a huge test of will to stay on there, but he did pretty well. Will keep practicing that with him for sure.