Out of curiosity though, if that is the problem, would a cheater plug on the amp (plugged into its own outlet as it is now) diagnose the problem...would I expect the hum to disappear if the separate outlet situation is causing the hum?
Yes, it might. With components that are connected via single-ended (unbalanced) interconnects, the interconnect shields serve as the return path for signal currents flowing between the two components. However, the component signal grounds, the component chassis, and ac safety ground (which is the ground prong on the three-prong power plug, assuming the component has a three-prong plug) are all connected together in the component (the chassis being connected to ac safety ground so that the circuit breaker will trip if an internal short makes the chassis electrically "hot").
Therefore any voltage offset between the chassis of the two components (which can result from their being plugged into different ac outlets or different ac runs or different surge protectors or line conditioners) will cause extraneous currents to flow in the shields of the interconnects between the components. The receiving component cannot distinguish between those currents and signal currents, and hum can therefore result.
Isolating the safety ground on one of the two components, using a cheater plug, will eliminate that voltage offset between the two components, since the only connection between them will be via the interconnect shields, and not via the ac safety ground wiring.
An argument could be made that using a cheater plug defeats the safety purpose of the safety ground (and in fact the author of the paper I linked to in my preceding post, who is a distinguished authority, makes that argument), but as long as one of the interconnected components is connected to ac safety ground, the chances of a problem arising as a result are remote.
When you try the cheater plug, if necessary also try both possible connection polarities of the ac plug.
Regards,
-- Al