I bought some electronics contact cleaner at Digi-Key (see attached picture) and, with the enpeg unplugged, tried spraying it into the encoder, via the gap between the shaft and the neck/collar. I dismantled the faceplate first, to make it easier to reach, and to prevent the spray from staining the lens or the vfd.

Immediately after spraying it, I rotated the encoder several times to make sure it was spread around in there. The stuff evaporates quickly. I let it dry for a few minutes and plugged the player in.

Result? Perfect encoder operation. Before, I was at the point where it was nearly unusable.

There is one variable unaccounted for so far. I haven't plugged the player back into the dash and tried it there yet. Since I didn't double check that the encoder was still glitchy when the player was on AC power before spraying, I'm not 100 percent sure that the spray changed anything. For all I know, plugging it into AC power could have been the thing that made the encoder stop being glitchy. I'll test it out tomorrow in the car and see how it does, and report back.

Either way, I have been able to go from bad encoder to good encoder without breaking out the soldering iron.