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Try the ammo. What ammo have you shot out of your M77? Are you a handloader, or do you know someone who is? Have you done anything to obtain or produce accurate ammo for your rifle?

I say this only because, altering the rifle should be a last resort. Removing wood is hard to undo. Various bedding solutions can offer improvements, but there is no guarantee. One should always start with the ammo, the easiest (and cheapest) thing to change and expiriment with.

I am not saying you should not free float your rifle barrel, only that you should not start there.

Ever hear the story of the guy who was about to sell his Steyr SSG cheap because it would only group about 5 MOA? When he was convinced to try some match ammo instead of the Philippine surplus he was shooting he decided to keep the rifle! try some different ammo, several kinds. After that, look to the rifle, if needed.

Also, check the crown very closely. Slight damage can cause poor groups, and having it recrowned might also be a solution to your problems. There are many things that ought to be considered, these are just some of them.

One last thought strikes me, have someone else shoot your rifle, maybe it is you. Or it could be your optics. As you can see, there are lots of things that it could be. I vote you try different ammo first.