LX5000/AR4201 interference

I have a very strange interference problem with my
LX5000 and Becker AR4201 radio: when I transmit, the
LX5000 changes pages, menus and inputs on its own.
The funny thing is that if I hold the PTT and keep
silent, nothing happens: problems come when I start
modulating (talking).
The wiring has been double checked and found ok.
The two instruments are placed very close together,
with the LX directly above the radio, and virtually
no space in between.
The panel is carbon fibre.
The microphone is of the panel mount type, but insulated
from the panel surface.
LX Navigation could not find a solution so far.
A friend suggested I wrap the LX in a fine brass mesh
and connect this to GND (to shield it from electromagnetic
interference), but I am unsure.

Any competent suggestions?
Thank you,
cheers

Flavio