What do you have for an antenna? A broken coax shield could do this. Another is poor hood grounding. Try running at least two ground braids from the hood to the firewall, leaving just enough slack for the hood movement.
Two-way shops normally have add on springy contacts that you screw to the hood or fenders so that when the hood closes, ground shield is improved.:glasses7:I haven't thought about this in years, but your comments reminded me. My sister had a 67 Mercury Cyclone 390 back in the day. The radio would have a similar interference at idle. They came with fiberglass hoods with a metal mesh/screen in the fiberglass (if memory serves me) that was supposed to prevent it, but it didn't work 100%.
She took the car back several times, but the dealer didn't have a fix.
Hope you find the culprit Rusty.