. I used to have a real problem with a comm radio which would stomp out the whole panel when the microphone was keyed. GPS, LORAN(C), ADF, and VOR/Localizers would just go haywire. There had to be a wiring error there somewhere; the only way I've seen that RF can affect all those devices simultaneously is when the coax wasn't firmly in the comm radio and RF was seen/present *in* the cockpit ... broken shield, improper connector installation ...
It turned out to be two things. The first was a bent over pin in the tray connector. The second was some wire routing on the firewall and funny enough, a wire going to the altitude encoder that had a broken shield in the wire. In Cherokees they are mounted up front. Usually right near the blow-by vent tube(nice huh?)
You're right though by symptom, that being a short. Bent over pin.