Don't use tuner cleaner (quick way to ruin the part), and don't try spraying anything down the shaft (another quick way to ruin a pot). It depends on the type of pot used, some may respond to a TINY spray of DeOxit D-5 into the slot where the terminals exit, but some are sealed. Did I mention TINY AMOUNT, less is more in this case.
It COULD be a dirty pot, but it sounds more like a pot that has mechanical damage. The proper repair is to have the pot replaced.
Now the challenge with this amp is that it uses a custom motorized pot and i don't believe it's even accessible for cleaning. It's a nice amp, this is an example of an amp that I would take to an experienced, qualified GK service center that has access to factory parts and support. It's worth repairing IMO.