If it's scuffing .311" I'd leave it alone. Most properly-cut .308 Winchester chambers will peel rings off of a .311" bullet, so you can ignore my advice except for the part about doing a pound cast, which will eliminate any doubt or guesswork about what you need to size to. It will also reveal some potentially limiting factors involving chamber neck diameter, which is really about to come to the forefront now that we know the throat entrance is a lot larger than it should be.
Speaking of Remington anomalies......look up the 300 AAC Blackout chamber drawing on SAAMI's site and see where you could possibly fit a .311" bullet, other than all the way down into the case. Something is rotten in North Carolina. Fortunately, you can hand-load and make up for all that. In a lot of ways, the large throat entrances actually work in your favor, provided the chambers line up with the bore and the necks aren't terrifically oversized.