Pics. Sorry its mess right now. Been trying diferent wires and need to clean it back up once I fix this.
You are falling into a common trap, of adding and adding grounds, that seldom solves the problem.
You now have a complex system, and to make this work and have a silent background, then you have to design a ground plane and that takes skill and expereince.
It is clear to me that plate amp ground is not at the same potential as the rest of your system. That is caused by a resistance to ground between the receptacle the plate amp is plugged into and the rest of the system. So you best bet is to power that plate amp from a cable going back to your main system.
The more complex the system, the more likely you are to run into ground loops.
One approach might be to lift the ground in the xlr plug at the plate amp connection.
You usually solve these problems by removing grounds and not adding them paradoxically.