There is a type of Kevlar fabric made for archery targets call Spyderweb. It is designed for the fibers to spread apart without damage and then arrows can be pulled back through.
I found one report of somebody shooting it with an airgun and it didn't poke a hole but no recollection of caliber, power or number of shots it was able to withstand.
If you could put something like that over the front of the target and hold some rubber mulch inside I think that would help a lot.
Similar to the self healing rubber are the self healing foams. Also used for archery. I know a few people have used them for airguns but as I recall not a lot of information about their performance.
If it were me I'd probably use some corrugated plastic taped over the front with a thick and wide window flashing tape or possibly house wrap tape. Place the trap on its back, fill with rubber mulch, and the tape the plastic over the mulch. Completely cover the plastic and entire face of the target area with the tape as I feel it does take a bit of the smacking sound away. I would remove all of the duct seal and use the sound of pellets hitting steel to be an indication that you're getting tunneling or settling with the mulch. Not sure how deep your trap is but it probably won't happen often.
Another option to the corrugated plastic are those plastic garage cans. They have semi self healing properties of sorts and you can cut them up and get several pieces of plastic from them. Even a multi pump BB gun will shoot through them at 12 yards so no I can't image bounce back will be a problem.
My pellet traps are large as I like to be able to tape the game style targets onto them for my boys. If I could get away with a smaller trap I would use the garbage cans as the face of my traps. I could cut them up and flatten them with a heat gun but haven't tried it yet.
