Like you, I think the outlet grounds on different power circuits are at fault. Rather than spinning wheels trying some cheap device that may or not work, and which might compromise sound quality, I would simply run a room to room extension cord, plugging both systems into the same electrical circuit.
If it works, unplug and roll it up when not in use. Eventually, do the necessary adjustments at your main circuit box with your now proven concept.
This happened to me between my PC in the neighboring room to my USB DAC, which was on a different power circuit. The extension cord fixed it, and it now runs through a hole in the wall.