Hi Matt,
I experienced the same issue with the same radio and also with an EFHW, so I can elaborate about this issue and my solution.
When it happened the first time, I was on 17m and the antenna feed point of the EFHW was maybe only 1m away from the radio. When I disabled the audio compressor, the issue went away, but this was not the cause, it just “amplified” the issue.
I usually use 5m of RG-174 coax (again, like you I hard-wire it to the coupler).
When I experienced similar issues on other summits (always on higher bands), changing the coax (e.g. putting it more flat to the ground) and increasing the distance to the antenna, usually helped.
But I wanted to implement a robust solution and therefore I looked for a small and light common mode choke (CMC). Before building something myself, I always check if there is some commercial item available, either for inspiration or because I’m lazy 
.
On eBay, I found a small and light QRP CMC with a BNC plug and socket. Unfortunately, as of today, the item isn’t available anymore on eBay, but since you now have the image, you could use an image search to find another source.
Since I use this CMC, I didn’t experience any RF pickup anymore. It’s now part of my setup, also for other antennas.
73 Stephan