Test it on the Gamepad Tester.

After 7-8 tries of varying results, I was amazed that it worked.

Disclaimer: I am guessing that this might be a temporary fix. Although I don't quite know the initial state of the carbon tracks, the seem worn and I'm afraid the jitter might return.

If so, I would definitely try to replace the carbon tracks and washers first before going into soldering town.

Good luck!