...With shorting plugs in the input and not powered on, the Seduction buzzes pretty bad. ...
That's a big clue!
I've lost track of the details in this thread, but you can only know that with other things downstream of the Seduction. Most likely, here's what's happening:
Something downstream has a power transformer. That transformer's primary has some capacitance to the secondary which goes to the power supply
and signal ground. That capacitive coupling induces a current from the ground of the device power supply, through the grounds of the interconnects, to the chassis ground of the Seduction which is connected to safety ground. The voltage drop across the resistanceof the interconnects, RCK\A jack/plugs, circuitry, etc. creates a voltage which is amplified by the downstream device(s) and is what you hear.
There are other possibilities. It's possible that the neutral and hot are reversed at the power socket, so that the neutral is switched and the hot stays connected when it's switched off, causing some ground current from the Seduction.
It's also possible that it's radio frequency pickup, with various bit of metal acting as an antenna. You can check this by unpluggin the Sediction from the wall. If it still buzzes, you are picking up an environmental sgnal which is detected by some device downstream - probably the first one.