Chiming in here as I had a very similar problem, and wanted to help out anyone else who shows up at this page by punching "RV-12 GTR-200 audio feedback" into a search engine
I would get a squeal when transmitting, especially on lower frequencies, and when transmitting my voice always sounded muffled/tinny (especially so on a Bose A20).
What resolved the issue was simply removing the radio from the panel and reinstalling it. There was some grey dust at the bottom back of the housing which I brushed off with my fingertip before putting it back in, which looked like it was in the same general area as the grounding pads on the cage. All that's needed is a long 3/32 hex key, and following the directions in the installation manual.
Repeatedly fiddling with combinations of ICS/Sidetone/Radio Volume/Headset volume sometimes mitigated it, but there were still many instances where ATC said they couldn't hear me.