Update 1/5/11:
I recently added two more dampers to the joystick. I totally changed the way everything is mounted also.
To connect the dampers to the shaft, I used a rubber o-ring that the dampers fit perfectly on. I then cut the o-ring to the right diameter and used wire to hold it tight around the shaft.
To connect the dampers to the outer "ring", I used heat-shrink over the existing holes, then made a small hole and inserted a "j-hook" through the new hole in the heat shrink plastic. The j-hook then screws into the wooden "ring".
I also soldered all of the wires inside the joystick handle to a 34 pin IDE ribbon cable. This cable comes out of the bottom of the handle then connects to the base of the joystick via a connector I mounted on a project board. I soldered the existing 20-pin connector to the board. I removed the twist pot and the throttle pot and they will be mounted remotely via a cat 5 cable coming off of a pigtail on the IDE connector.
With all that, I am able to remove the handle and simply unplug it. It also gives my the opportunity to totally change handles if needed in the future.