Has anyone tried to open the camera (there are only two screws, as disassembled here: https://www.youtube.com/watch?v=lOU6rBUK0Do) and see if the position of the microphone wires have any influence on the hum? It is possible that they were incorrectly placed when assembled and are too close to some circuitry.
Obviously, this operation will void the warranty, so only try it if that's not an issue for you.