Will,
As you've said, it hums even when disconnected, so it cannot be a relative grounding issue between components. Done with that one.
You've also said that it has a 2 wire plug, which I think some of the other responders have missed. Using a cheater won't change the grounding worse than it already is - it's not using the dedicated ground pin. If the 2 wire plug is not polarized, then just try flipping it and see if the hum goes away. (I bet not). But I assume it is polarized and you cannot do that. If you can use the cheater and IT is not polarized, then you can try the same thing. Perhaps the JBL is wired wrong inside. At least it would be easy to check with the cheater routine. You won't set the house afire with that test.
Good luck
