RF co-ax should be grounded at both ends.
Screened audio wiring should be grounded at one end only.
I will go for a bonding issue with the radio boxes.
It is probably some sort of prop modulation or screening that is always there but does not show up with a good installation.
What is the range of the radios when airborne? Is it a lot less than it used to be?
Do a bonding check with a bonding tester, (they used to have a double probe and a single probe). I think the readings should be 0.02 ohms or less.
Do a check of all bonding including engine to airframe and all components.
Remove all earth connections, clean the metal and re-make the connections if there's any doubt about the bonding.
I'm a bit rusty on this stuff. It's over 30 years since I did installation and maintenance on these things.
Good luck.