I've tested with 10k pots and 100k pots. They both work, so the xbox360 controller must use voltage. .
The controller does not have a built-in deadzone, at least not when connected to a PC. (I don't have an xbox to test on)
So the deadzone is either set by the xbox or the game.
I'd test it on a pc, then on a variety of games to see if there is any difference in the dead zone.
Personally, I think it's the game.
However if that's not the issue....
One thing to keep in mind is that the pots in the joysticks are made to sweep from 1-10k over a narrower range of motion.
Let's say 90 degrees for the sake of argument.
You're only using a small portion of the full travel of the standard pots which probably have to travel 300 degrees to do the same 1-10k.
The xbox is only seeing the joystick move a little side to side, not it's full travel. So the deadzone will be larger in relation to the limited range being used.
The way around this would be to use 100k Happ pots for Happ analog joysticks.
They have a custom taper and range of motion similar to the original xbox pot.
http://na.suzohapp.com/amusement_products/accessories/50-2032-00I ordered ONE hoping to get a part number off of it and get it cheaper elsewhere.
The numbers is "built to order for customer" on the manufacturer's website.
If this is the issue and the throttle and brake work ok, maybe you could get away with only having to buy two.
I've never tried mixing 10k & 100k though.