The AGC circuit is probably the culprit. In most receivers the AGC voltage is taken from the detector. The dc voltage is derived to be proportional to the average level of the carrier and adjusts the gain of the radio-frequency (rf) and intermediate-frequency (i-f) amplifiers. The AGC tends to keep the input signal to the audio frequency amplifier constant despite variations in rf signal strength. Remember that all circuits have an inherent "self-noise", so, given we are losing signal due to the shorted-turn effect, the net result is to run the receiver at very high gain, hence the noise.
This theory fits as far as the new antenna on the aircraft underside NOT being so affected (out of the shorted-turn ADF antenna influence).
So what doesn't fit?
The only part I'm perhaps struggling with is why turning off squelch does not seem to produce the same "noise" on an open channel; i.e. tune off station, defeat the squelch and I would have expected a similar noise experience (since the AGC should ramp the receiver to max gain). However I have not looked at the specs or circuit of the radio in question and there are various tricks of circuit design to prevent ''no-carrier-at-all" situations blasting noise... so that may be it.
Whilst you are surely on the money saying that there is a good chance that an AGC circuit is actively involved in this issue, I think we have to once and for all get away from the idea that this an adative Signal+Noise on the audio problem. Surely the Squelch experiment clearly demonstrates that there is no constantly present unusual noise source, but instead something more akin to an AGC oscillation/instability and/or unusual modulation phenomena somewhere in the signal chain that is induced as a result of some mechanical phenomena near to the actual antenna. The ADF wire removal is going to provide to some very good data.
p.s. THANK YOU John_T!