My guess is that it is not the seat itself, but maybe the floor where you put your feet. I think your rear speaker wires are probably under there. This is the only reason that I can think why you would have stereo interference that far away from your stereo, unless you have an external amp, under the seat. Maybe your rear speakers are grounding out and you are pulling those wires when you place your feet on them. I would look under the carpet and see if there are speaker wires there. It seems like the PO used the non-stock harness, and didn't wire the speakers along the rim of the body, instead they were wired under the carpet. It is done that way to reduce wire length. My installer did this and I changed it.
If you ever want to remove your carpet, you will have wires under you. This is why I rerouted them. Plus, the reasons that you stated, with possibly damaging the wires by rolling your feet on them and smashing them with your feet. Also, maybe they have been moved by these actions and pulled loose from the back of your stereo.