So I got the joystick from Grayhill, seems perfect for the job. One complication is that there's only one signal wire for each axis (left/right and up/down) that's either at 0, 2.5, or 5v, so some minor circuitry is going to be required to get a 2 bit value for each out of it.

The other problem is that they're $62 for 25-99 and $49 for 100-250. If there's enough people interested I can put together a group buy... Maybe I should post this in Technical.