As it turns out, it was indeed a faulty 3PDT switch. Replaced it and it’s all good now!
I bought it from the Trading Musician, which is a pretty reputable local shop. I tested the switch with a continuity tester and did not see any faults with any of the terminals, or “subswitches” as you call them. I’ll try your power disconnecting method, although I don’t think that’ll work since this pedal uses a 3PDT switch so I’m guessing all the switching/bypassing is mechanical?
I guess, since there’s no warranty and the shop probably won’t let me return it since I was stupid enough to velcro it to my board before giving it a thorough test, I’ll try replacing the switch. Otherwise, I guess that’s a $100 lesson.
Wow, nobody?