I don't know why I've never thought of this before, though it's probably because I've basically given up on the issue thinking that it was RFI from the car, but I have a couple of baofeng bf-888s laying around that haven't been used in a while, and I thought I'd give one a go in the car today to see what happens.
I plugged the mag mount antenna to the radio and drove the same routes that I always do, listening to the same repeater as usual, and shockingly, there was no geiger counter noise. RX was so much cleaner, albeit the crappy speaker in the unit was on the verge of distortion when I had to crank it up to hear it over the road noise.
I think it's pretty clear, at least in my case, that the issue lies with the uv82hp radio itself, and that my car is actually pretty quiet as far as RFI goes. The mailman will be dropping off a new uv-50x2 today, so I'll be plugging that in tonight and see if there's an improvement.