I bedded a .22 RF (Remington 541-S) using Devcon Flexane back in the 1990s. Turns out Flexane will take a set -- the rifle leaned up against the side of the safe, and the bedding changed. Since this is a long way from ideal, I rebedded it with two small "hard points" -- regular epoxy, like Marine Tex, or Devcon Steel. The rest was done with Flexane.
This worked rather well. Did a friends 541 heavy barrel with the same technique. Both shot quite well -- esp. after gluing the barrel to the action instead of relying on that silly pin.
There are more Flexane products out there now, maybe one of them would work without moving around. If not, it's like a KICK-EEZ (Sorbathane) recoil pad. It's gonna change shape, so you need hard points where the screws go.
Never tried this with a CF. IIRC, Browning did use some form of rubber bedding with the original BOSS rifles.
Not much help, I imagine...