Excellent question. The joystick travel, lock to lock, is actually a very small portion of the overall travel range of the potentiometer. I haven't got an easy way to measure it, but it seems like it's probably something like 45-50 degrees worth of total travel. So the pots in the joystick are only using a small pie slice of the total capabilities of the pot. So it would make sense that if the tolerance of the pot varied by as much as 10 percent, then I'd indeed expect it to make a visible difference like the one I'm seeing.

If I were the one designing the thing, I wouldn't use cherry picking to get homogeneity. I'd fix it in the electronics or the joystick firmware. For example, via trim pots on the circuit board (I didn't see any but I'll double check), or write the firmware so that it corrected for pot variance over time.

I briefly tried adding a second pot to act as a trim pot, but it made things worse and was too fiddly to be able to make a good adjustment anyway.

I think it's probably actually OK in the game, and I don't really need to do anything to correct this, most of this is just an interesting tech exercise for me.