I actually did manage to clean them in the end. I started poking around at the one I'd desoldered, and I guessed that it was only welded at the corners if it was at all - the moulding quality is very high, so they fit together almost seamlessly. I wedged a set of flush cutters in and managed to pry the top off. I immediately regretted this decision... 14 tiny wipers went flying across the desk.
I don't have any images of the inside of the switch (left the camera in high speed video mode... about 10 seconds of footage), but I found an image online.

The encoder disk was filthy. The wipers and disk are silver plated, but they had some orange/pink tarnish or deposit all over them. On the one I desoldered cleanup was rather easy with nutrol and IPA, but reassembly took over an hour due to the tiny pieces and no idea what order they were supposed to be in. Ended up sticking all the pins in a protoboard and soldering them down so I could put the disk and case back on.
For the other switches I just left them in the board, took all the panel buttons off and pried the top case and spindle out, leaving the wipers and disk attached to the board. This made cleanup a bit trickier (lots of electrosolv and IPA wetted paper) but reassembly was a snap. Put everything back in the case, and I have almost perfect horizontal and vertical control with no skips.
Tested the voltage rails with a multimeter and they're all within 0.5V of where they're supposed to be. 15v showed up to 100mv on AC, so that's where I'll start with the scope this weekend. Tried adjusting grid bias as someone had suggested before, but didn't end up having any effect on the ghosting or shudder.