I just thought I'd post and thank you guys for all the help!
He started to eat pellets finally, so now I reserve the bloodworms for treats. And a day after that he made his first bubblenests, and now he makes them regularly.
The aquarium salt wasn't causing the scum, because I didn't add it once when I cleaned his tank... and I ended up with an unhappy betta and that persistent scum. So I'm back to the salt, and I just can't figure out what the scum is coming from.
Also, I cleaned his tank yesterday and now that he's used to his new home I put the clay pot back in. He seems to be tentative about it, but he's starting to like it. He still likes to hide behind his plant, though.
I've now had him for three weeks, and he's definitely settled in. I am a very proud betta parent now.