Hum with balanced cables

If you running balanced cable between balanced connections, then why would you say that you 'properly' set the amp end to unbalanced? Likely that bal/unbalanced switch would be doing the same as tying pin 3 to pin 1 of the XLR.

Without a schematic, it's guessing but I would wonder if you had one leg of the balanced connected to ground (via that switch) causing really heavy load on the preamp output. Shorting an active output can blow it, cause very high distortion if it has enough output resistance built in to survive or cause various audio problems due to the pre's output stage trying to blow. Normally I wouldn't think a buzz/hum would be the description, but might show up that way.

If Parasound does the XLR pin 3 right and doesn't share grounding between the chassis, then the ground lift should be able to be closed on the amp and both the pre and the amp share a hopefully common ground reference from the power ground. Using the same power source is important in most cases. Depending on other components hooked to the pre, things could change for grounding though so ungrounding the amp might be necessary (hence the ungrounding switch).

Balance has a number of positives and should not be going in the direction of any kind of increased buzzing or hum.

CJ

I never ever got a hum with any balanced cables in my entire life . By Design Balanced cables have the lowest noise floor compared to unbalanced. It is not physically possible for a un balanced cable to have a lower noise floor by design.
You have noise in your power I feel. Something is injecting a EMI signal into your system. It's not the cables it's absolutely something else unless you purchased bad cables.

Your next step is to get multiple dedicated AC circuits. One for the preamp, CDP, etc., and one for each amp. And don’t plug non-audio junk into an audio AC line.