I am surprised the 22 went thru it at 100 yards. I have a mat like that and it is pretty dense. I would call around for a sheet of plate steel and be done with it. Or maybe a 2nd mat behind the first.
Skin the back side of your frame with 3/4" plywood, and fill the inside full with rubber mulch from your local HomeDepot / Lowes / etc. keep the rubber truck mat on the front side. (might need to do a couple of center supports to the frame interior, to prevent the truck mat from ballooning too much).that should make for a fine trap that is fairly quiet too.
A few layers of heavy carpet or canvas hung from the top, with space between them, in front of the mat can absorb a lot of energy.