No advice to offer about the direct-to-amp hum without being able to check out the amp in person.
For the pedalboard, it sounds like the earth on the power supply transformer is connected to the signal earth, giving you the earth loop we all know and [i]don't[/i] love! The solution is to keep the safety earth connected to the transformer primary, but break the connection to the secondary side of the circuit. I had this issue with a Harley Benton Power Plant - to fix it I just needed to break a track on the circuit board. This left the safety earth connection intact, so the metal enclosure is still earthed via the mains cable, but left the 9-volt outputs 'floating'.
WARNING: Don't attempt any mods like this unless you know [b]exactly[/b] what you're doing!