I agree that you've gotten some good suggestions here.
Other things to check:
1. Loosen the stock screws and take the barrel in one hand and forend in the other. Move the barrel sideways within the barrel channel and see if the action moves around in the stock. If so, it should be glassbedded.
As a temporary measure, try putting a couple of layers of black electrical tape on the receiver at 4 and 8 o'clock (analog). Set the barrelled action in the stock again and re-try moving the barrel. If it's still loose, add another layer and try again.
2. Remove the pressure pad with sandpaper wrapped on a dowel. Reassemble and tighten stock screws adequately, but not to the wood crush point. (Despite many tries, I haven't had good luck trying business cards under the barrel to improve accuracy.) Free-floating is usually best!
3. When shooting from the bench, use a slip-on recoil pad, or a sand bag between you and the rifle butt.
JP