Bryan Martin wrote:

All of your audio shields should be grounded only at one end, ...

And finally, your audio jacks should not be grounded,
they should be isolated from ground by plastic washers and grommets.

This is all correct, but it may not fix the OP's problem. Sounds like
transmit RF might be getting into the low-level audio wiring, in which
case the shielding may do the trick.

If you have a bad antenna installation (poor antenna
grounding/counterpoise/internal antenna, high VSWR on the coax running
from the COM to the antenna, or if the coax is bundled too close to some
of the audio wiring), the transmit RF can couple into the audio wiring,
and get rectified inside some of the audio equipment (audio panel,
intercom, or mic stage of the COM itself), causing a "howl" or "squeal"
only while transmitting.

If this is the case, checking/fixing the antenna to reduce VSWR and
resulting radiation off the coax is first priority, rerouting coax more
distant from audio wiring is second, shielding the audio wiring is
third, and putting some RF bypass caps or RFI suppression beads on audio
inputs is fourth...