I'm trying to get rid of a 60 cycle hum when the AMPS [emphasis added] are on...
More detail is needed. First, are you saying that you are using a pair of monoblock amps? Also, what model is/are the amp or amps, and the sub? And am I correctly interpreting that you are connecting the sub using its speaker-level inputs, and that the hum is emanating from the sub?
Also, some of the vintage McIntosh amps have both a "gnd" (ground) terminal and a "com" (common) terminal adjacent to their 4, 8, and 16 ohm output terminals. If that is the case here, which one of them are you connecting the REL's black wire to ("gnd" or "com"), and is there a jumper on the amp between those two terminals?
If both of those terminals are present but there is no jumper between them, adding a jumper may fix the problem. That possibility is reinforced by your statement that the two-prong adapter made the hum much louder.
Regards,
-- Al