I've used stainless foil to wrap parts for heat-treat, very thin foil.
This came to mind as I read your question.
Perhaps a small local bit of such foil at the flash hole on your stock..?

Is there even a few thousandths of an inch gap there between wood and metal where you could set a bit of foil?

This foil could be removed and discarded after each hunt.

Just a thought.
Never tried this myself.

Cheers
Tinker