Sorry for the double post.
Ok, I talked to a buddy of mine who knows a thing or two and he told me I should put a capacitor in parallel between the wiper and ground of the variable resistor. I found a 10 nanofarad ceramic disk cap and soldered it in (from what I learned, when looking at the back of the controller, the right pin is V+, the middle pin is, obviously, the wiper, and the left pin is GND, so I put the cap between the wiper and the left pin). I wrote a simple Arduino sketch that will pulse a pin between 20 and 60 (which equals out to .35V and 1V, 40 would be .75V, or dead center) and at the same time turn an LED on and off (so I can know when it's switches, light on means it's telling the controller to look left, light off means right). I've got the controller plugged into my computer with the Wireless Receiver and I'm monitoring it in the Game Controller Properties. When it switches, I do see a change in the bars, but it's really erratic, not a smooth change from one side to the other.