Ken it's your rifle.
I did not see any change in accuracy in setting the bullet deeper ahead of the case. When I finished the session using 50 rounds from the case making contact with the bullet base to extending the seating ram 1/8" past the case mouth the worry about a possible ring is not worth it.
I do see a good increase in accuracy when I breach seat the bullet with increase in diameter of the patched bullet when increasing it from bore by one thousands diameter steps changing the paper thickness. .004" over bore is a lot tighter grouping than bore diameter when breach seating.
I scoped the chamber with the Hawkeye with 24X magnification and no signs of damage. But there is always the........