I wonder if it would be possible to build a firmware/hardware solution that would translate one type of input into another like the way that joytokey changes gamepad inputs into keystrokes.
Seems like it would be fairly easy to make a 360 degree wheel to 270 degree game converter that would translate optical transition right/left inputs to increases/decreases of either:
1. A potentiometer-style voltage output (for input to a game PCB/console gamepad hack)
2. A USB HID analog gamepad axis value (for a computer)
The main downside is that you wouldn't have any mechanical centering.
The tricky (impossible?) converter would be a 270 degree wheel to 360 degree game.

Just spitballin' here, but maybe use some code that translates changes in the difference between the potentiometer voltage (0-5v) and center (2.5v) into optical transition (quadrature waveform) outputs.
In the large central portion of the range of motion (
___|___ below), the outputs could correspond directly with changes in the voltage (i.e. each 0.05v increase/decrease = 1 transition right/left) -- no transitions when the voltage is steady.
At the outer portion of the range of motion (
*** below), quadrature waveform left/right transitions are sent continually even if the voltage is held steady.
The further you go from center in the outer portion of the range of motion, the faster the transitions are output, kind of like using a potentiometer and 555 timer to control how fast an LED blinks.

0v 0.5v 2.5v 4.5v 5v
|
***|
_______|_______|
***|
Like I said, just spitballin' here, but maybe there is an idea here that someone can refine/rework into a usable application.

Scott