So, just to follow up, I think I figured out the problem. There must have been some gunk in the pots that was causing a problem. I bought some DeoxIT that arrived today, so I hit the pots with it, particularly the volume control. I let it dry for a while, closed it back up, and now it behaves like it's supposed to. The volume actually changes when you turn the knob, so hooray! I think this poor module must have seen some abuse (smoke?) because now I noticed that the program/parameter button isn't always registering. Ah well, the beauty of vintage synths, yeah? It's all good, I've been enjoying playing it.
Thanks for the suggestions!
- Mike