Radio squeal

I know this subject has come up often in the past and I have checked
back on most the old postings for a cure but still don't seem to be
able to solve the problem.

The aircraft is a Koala (Fisher Products, all wood and fabric). Radio
fitted is a Narco Com 810 with Telex headsets. (I know it's not the
best but I have to make do with what I got here).

The setup squeals intermittently when in TX mode. When I say
intermittently, I mean sometimes its quiet, depending on which
position I'm sitting in or whether I'm moving my arms or depending on
whether the headset cable is draped over my shoulder or lying in my
lap or lying on the seat beside me. If I touch it, it squeals. If I
move it around, it stops. If I touch the coaxial cable it stops
squealing, or starts, whichever way round. It's as if its acting like
an antenna emitting a signal when its being waved around.

This is what I have tried already:
1) re-made the antenna with new coaxial cable and fittings.
2) made up a new groundplane for the antenna.
3) checked the VSWR with a 2 meter ham SWR meter. The reading is just
a touch over 1.5:1 on 122.600 which is my airfield's frequency
4) checked all the ground connections and fitted .01µF ceramic disk
capacitors from the audio line to ground and from the mike line to
ground.
5) fitted a small 470µH RF choke to both the mike and audio lines.
6) replaced the headset mike and audio lines with new, individually
shielded cables.
7) de-soldered and disconnected the microphone from the circuit inside
the earcups.
8) de-soldered and disconnected the headphone speakers inside the
earcups.
9) re-routed the coaxial cable.
10) tried coiling the coaxial cable
11) I have NOT tried another radio, because that will probably involve
a rewiring job on the panel.
12) everything works off a 12V DC power supply (automobile battery)

What seemed to work fine was when I plugged a "rubber ducky" antenna
straight into the radio, thereby eliminating the length of coaxial
cable which runs to the roof of the aircraft. When the "rubber ducky"
is connected to the outside of the aircraft, on the roof, in place of
the proper antenna, it squeals again, which tells me it has something
to do with the coaxial cable and heatset cables radiating, inducing,
feedback,emitting (whatever the right word is) into things.

Anyone got some ideas I haven't tried yet?

Gerrie