All this is
assuming that the pot is connected as above..
Use your multimeter to check the connections on the XBox pot pcb pads.
As I said,
IF it is connected like a 'normal' pot you will have three pads.
A high - hopefully Vsupply
A wiper - the one that varies when you twiddle.
A low - hopefully ground (0V ref).
Obviously at any specific pot postion both the 'high' and the 'wiper' will vary with the supplyV - assuming no regulator.
An easy maths example.
1. The V supply is 10V, you measure the wiper = 5V. Pot at 50%.
2. Battery droops to 6V, you measure the wiper = 3V. Pot at 50%.
So, by measuring the pot high side with an ADC and measuring the wiper with another ADC you should be able to scale the wiper position.
Basically if the wiper ADC is half the High ADC then its at 50%. Yes/No?
Its just a suggestion ASSUMING the pot is wired in the traditional manner.
If it's not then I've just wasted 20 minutes