Jay, the 20 minute delay on another outlet is totally puzzling, so no further comment. If you disconnected the cable feed and still got the hum, it's been found not guilty and there'd be no purpose in getting the cable isolation transformer. Since you mention splitters, apparently it's connected to several TVs; if any of them are grounded(3-prong plug in separate outlet) and are also connected to the other components with an interconnecting cable(wire, of course, an optical connect won't form a ground loop), this can form a ground loop. If you didn't already do so, disconnect their power cords(even if they're turned off) to check for hum. Yes, it'd sometimes hard to trace the loop, but disconnect everything until you get to the point where it's gone.
No, using the cheater can't possibly damage the equipment, but it could possibly damage you. If the amp isn't grounded through its power cord then it's grounded through any interconnect which runs to a component which is grounded. This may or may not be an adequate ground, although you read of some who use the cheater plug except on one 3-prong grounded component, and rely on that for the entire ground.
