Well it turns out I had very few of the necessary caps on hand. I mostly work on older sets and only stock 630 volt caps while this set has a few 1,000 and 1,600. Oh well, I'll just have to wait a few days for my order to arrive.
Meanwhile, I discovered why the sound was stuck at 100% - the volume control is bad! There's no continuity to the wiper. I cleaned it with DeOxit, but that didn't help. Then, I pried back the tabs and opened it up for a look inside. It seems there wasn't enough pressure on the wiper so I bent it a bit. After reassembling it worked better, but there were some dead spot. Also, I managed to break the push-pull switch somehow
So I started hunting around for a 1M with 500K tap plus push-pull switch with a suitable shaft. Playthings of the Past has some promising candidates, but before placing an order I figured I better dig through my spare parts box. Much to my amazement I found an identical, NOS control right on top
