A muff will certainly help - gives a little bit of extra isolation relative to the normal foam sleeve. I notice that many pilots don't use the foam, which compromises even closed cockpit transmissions when the boom is in the correct position (nearly touching the lips).
Another thing to check is the audio gain at various stages in the chain. Many transceivers and/or external ANR buggery boxes have default gain settings which are too high. You don't want any compression or clipping circuits to be operating with just the background noise. Every setup will be different but, with a thick foam mic sleeve I ended up backing off the insert gain a little, the external pre-amp a bit, and the ICA210 transceiver gain a lot.
I did what I could on the ground but finally used a scanner with a solid state memory to record CTAF transmissions, mine included. After a hour or two of listening to lots of transmissions I have new respect for the ATC folks!