The solution is new pots. CH still sells them for $10 each, and you need one for each axis. These pots are also good for old Thrustmaster items too.
While you're waiting for them, go to Radio Shack and buy a can of "Tuner Cleaner," part number 64-4315. Spray just a little bit where the pot shaft enters the body. Let it sit for a minute as capillary action draws the fluid in, and then rotate the shaft back and forth about 100 times. Try the stick.
If it is still jumpy, try it again.
If its still jumpy, shoot a little bit more into the gaps into the body and twist the shaft again.
If this fails, then you definitely need a new pot, but this will probably work. Or at least work good enough until the new parts come.
You're welcome. ;-)
-Llama