I shoot a Mark 5 ultra-light in 300 Win mag. I started off with groups around 1.5” to 2” at 100yds. I ended up spending cash and having the action blue printed, barrel free floated, cryo, trigger job, glass bedded. It has been shooting .5” groups ever sense (last 14 years). I also picked one up in 25-06 about 9 years ago. I knew more at that point and glassed it myself, floated the barrel and did the trigger. Also became a great shooter. I had many people tell me the ultra-light barrel would not shoot free floated, they were incorrect in both cases. Try a good glass bed for the action and float barrel, I did glass in under the camber of the barrel. The trigger is adjustable and worth looking at too.
I also discovered that the way I was absorbing the recoil was affecting my accuracy with the 300 in the beginning. It took practice to absorb the recoil consistently with the lighter rifle. Love the 300 take into the woods every year.
Good luck