Alright, I finally figured this out. The game actually has the capacity in its UI to change the sensitivity for each axis separately. You just have to highlight each axis' binding, which reveals a separate sensitivity bar. It's pretty un-intuitive, but wow, what a relief.
Now if I can just figure out how to get music going without my old discs, I'll be in business.
Someday I will be the most powerful jedi ever.