I would put the sound deadening material on the inside and just paint the under hood side of the firewall black.
If i ever rip mine down that far and actually fix all the rust and have a decent body, I even thought about doing bedliner from top of the firewall all the way underneath to the very back on the bottom side of the body. Plus maybe the inside of the tub on the floor and side walls, possibly inside of firewall too. Mines an M1009 though. no carpet or side panels in the rear. I also doubt I'll ever tear it down that far though!