I would try switching the recoil pad before a break. The pad is simple, easy, cheaper, less chance to mess anything up, then if you feel you need it try the muzzle break. Even with the pad it will still kick, but it should change it from a hard abrupt punch to a still hard but slower push, which is much easier to handle.
It might also be worth getting a second gun in a smaller cal to practise with and get range time in, then switch to the 308 at the end to keep up with it. This is usually easier on the shoulder and much cheaper in the long run as price for ammo for a 308 vs something like 223 or 7.62x39 can be quite different.