Larry, thanks so much for the ID of the pot. I was indeed hoping that the numbers printed on it would indicate its specifications. Where can I find a reference source for how to read those identification numbers? Some googling gets me a lot of links for guitar amps, and the larger pots in those amps seem to use different types of coding numbers. For example, though I see that "B" means linear taper, I don't see how "104" indicates 100K?
Thanks so much for the link, it will get me started on the right track. Though the particular pot that you linked doesn't look like the exact dimensions and shaft, I will start there and keep looking to find one with correct shaft/dimensions. You said that the picture doesn't show the keyed shaft, despite the part number being correct for a keyed shaft. I'm also concerned with the threaded neck, which might not fit the place where the joystick accepts the part. I'll keep looking to be sure I get the right part.
In the meantime, squirting some electronics solvent and isopropyl into the pot has gotten it working normally again. I will still find and order more replacements for the future: Cleaning only works on these things for a limited amount of time.