You could always try a brake. I know they are loud but if your goal is reduced recoil, there is no doubt they are very effective. I shot a CTR 308 with a APA Little Bastard Brake and it was incredible how much it reduced the recoil. And yes it was loud.
I put a SiCo Trifecta brake on my CTR early on so I could QD my Saker762. Turns out the QD adapter for the Saker isn't as repeatable as the direct thread adapter, the brake, on the other hand, worked so well that I've left it on. I am getting a little tired of the concussion though, even with plugs and muffs, it gets a little old after a 50-75 rd range session. Given the responses, from other CTR owners, I might just get the limbsaver. I've always liked how well limbsavers have tamed my other Tikkas