Hey, Jason,
I haven't shot a Shadow Sport, but the older S1K will shoot well from a rest if you use some type of gel pad. I've used a gel mouse pad, other guys have used gel filled bicycle seat pads. If you decide to try this, just make sure the rifle can still slip a little when it recoils. When I first tried this, I had the mouse pad sitting on a cardboard box for height. It was slipping around, so I taped it down. The groups promptly went up. I've managed near 1/4" groups with that rifle and setup at 20 yards. Give it a try.
Dave