Tweaking a martial gas gun for maximum accuracy requires more attention than spinning on a new barrel, even if it is an excellent barrel. Any of the accuracy enhancing techniques that apply to the M-14 family also apply to the Mini with a few additional considerations. The stock needs to be heavier for additional stiffness and of course proper bedding is essential. A good trigger does not make the rifle any more accurate, but you won't be able to shoot the rifle accurately without a decent trigger. The double pull should be maintained, and the trigger pull weight should probably not be reduced below 4 pounds.
I would like to see a rear sight similar to the M-14 National Match with a hooded aperture with a half minute adjustment in the hood, but I don't know if the Mini's design is compatible with the M-14 sight. I suspect most folks would just scope their rifles anyway.
I see no reason why a tricked out Mini-14 loaded with match ammo could not shoot .75 MOA or slightly under. Of course the same expenditure in a bolt gun will completely outclass this performance from the bench, but the Mini is not a bench gun and it could show well against a bolt gun in the game fields or in a practical course of fire.