Welcome to the Forum, Murphy!
You might try floating the ground in the balanced connections (i.e., clipping the shield from the connector at one end), but it sounds to me like your problem is probably “upstream” of the BFD and amp, like maybe a cable TV or satellite dish feed that’s not properly grounded. It won’t do to turn off everything in front of the BFD/amp. It needs to be disconnected from the BFD/amp. I’d first try disconnecting any cable/sat service antenna cables from the system. If that doesn’t isolate the problem, then disconnect each component from the system and then add them back one at a time to see where the noise starts.