I'd suggest powering the PICCOLO from the heater supply on the CORNET2. Eliminates the need for an extra power supply and possible grounding issues.
On the C2 inputs, it is only a hum issue when using 100 ohm loading on an MC cart. If you use 47k loading, you don't get the induced hum. With twisted pair wiring the problem isn't very bad, but it is still there, so not perfect.
jh