Now you got me thinking, that's not only painful, it's dangerous! It's bad enough when I come up with ideas like this myself, but now, you guys are stirrin the pot!
The bed- liner thing is sheer genius! I do remember something in a paint can that you dip tool handles in for a rubbery grip. And there is the possibility of stick on foam, something like camo tape.
So I asked myself, why rubber? OK, ok, I know, rain, wet, snow, ect. But when it's really cold, it ain't wet. Maybe a nice, cozy wrap, wool perhaps. Sorta like a gillie, camo wrap, with provision for the break action. One piece under the action, from the grip to the forend, and then wrapped fore and aft. Not hard to try, easy to remove if you don't like it, and above all, CHEAP!
H-mmm, got a piece of wool sock here, this might work.
Woodbutcher