@atmasphere -- Thanks for this. You're right, it's complicated. (You are also right that the grounding post made no difference.)
I'm starting to wonder if the problem has more to do with the DAC. As I wrote above, when I disengaged the preamp section of the amplifier to control the volume with the DAC output control, the hum came back, even though I was still using the modified power cord on the amp. But then again, this didn't happen with two other amps I had on hand.