When I use the stereo cable and separate amps for the magnetic and piezo pickups I hear a pretty serious hum. What can I do to get rid of this?
You have what is known as a ground loop. This isn’t the fault of the guitar or the amp. Ground loops can occur whenever two pieces of electronic equipment are connected. Use a Direct Box with a ground lift to isolate the two amps. Plug the Magnetic end of the Y cable into one amp, and the Piezo end into the Direct Box. Plug the Direct Box’s output into a balanced input on the second amp. Do not disconnect or otherwise attempt to defeat ground connections on your electrical equipment.