I agree with
Murphy
The problem occurs when the received signal is coming through the prop and the effect is the same on strong and weak signals. This rules out many possibilities.
What may be happening is that the incoming signal is modulated by the prop, quite literally mechanically chopped. This will put strong amplitude modulation onto the carrier. With a two blade prop running at 2400rpm this is 80Hz am. The modulation will be a constant proportion of carrier and so bear a constant relationship to the received signal (also am). Presumably the receiver agc sees the chop and turns the gain down, reducing the amount of wanted signal.
Kudos @murphy (pending confirmation!!)
The effect may be specific to a particular type of receiver or even to the mode of operation set on the receiver or the software version loaded. I don't have a schematic so can't even begin to guess what is going on inside the receiver.
I think we likely have a winner. I'm not sure if we ever got a result from @hangflyer for the experiment to connect the handheld to the aircraft antenna, but I'm not sure if that would be conclusive anyhow for exactly the reasons @mike-wsm just spelled out, namely that this kind of AM modulation might play havoc with only some AGC designs. @hangflyers other observations now rule out a whole bunch of other possibilities, we don't have an independent noise source. If it proves very difficult to locate the grounding issue for the prop, I wonder if just relocating the antenna to a position that has an aharmonic distance relationship to the prop will work around it? I probably shouldn't be suggesting such kludges...I'm just curious to see if the modulation effect is working the way I imagine.