I'm suspecting the remote lead from the HU. Connect the remote for the amp directly to a power source and see if that eliminates the problem. If it does, you may have to replace the HU or power on the amp in another manner. Or, use your volt meter to test whether or not you're getting at least 12volts from the blue/white wire.
The issue with noise when moving the wakeplate makes me think poor power supply, be it hot (+) or ground (-). Be extra certain that you are properly grounding and the amp isn't trying to ground through the remote wire.