I did something similar in an optimization class in college. To stick with the theme of not going into the math, I won't post my slides or report. Rather than using the "KontrolFreek" method, I decided to replace the entire joystick. Below are some pictures of the finished project. If you want the .stl to this one, I'm more than happy to share. I don't know where the CAD files for it are though...
If I were to improve on this design, I would make the base of the joystick thinner and probably spray the top with plastidip. I find that my thumb travels a lot along the outside of the joystick, so the contoured thumb grippy thing would not be beneficial for me.
Before cleanup (acetone vapor bath) and installation:
Right joystick is new, left is old:
