Did some research on guitar feedback. Suspect the pickup lid is vibrating against the coil itself. The other guitar kit has no lids. Opened up the pickups to see how they are assembled. There is nothing between the pickup coil bars and the cover. Some people use wax to pot the lid on and dampen out the mechanical resonance of the lid.
Wax isn't ideal in AZ, instead I used a minimal amount of silicon only around the edge of the bar where it can contact the lid. Solder lids back on and the feedback/squealing issues are gone. Now can turn up to 11 and enjoy. Guitar is cheap, but with some care and minimal money I was able to solve the noise and feedback issues which otherwise ruin the instrument.
I left the pickup wiring as is. Could have removed the wire shield from the pickup baseplate (which is soldered to cover) and ran different wiring. Ideally that would be a shielded pair, which I could make, but don't have anything appropriate at this time.
Pickup baseplate/cover connected to star ground with regular wire.
Pair of signal wires and shield to their respective pot. Shield connected to pot ground/case that is already grounded to star with it's own wire.