I have checked everything you stated. I'm thinking its the pencil thin barrel. The coating is cerakote. Im going to scrub the barrel and give it one more try. After that i'll be letting it go.
You've swapped out to a known god scope and it won't shoot?
Beyond that, search these forums for "BTE regimen" and follow that. Be prepared for a ton of copper and for it to take a long time.
Check the crown for burrs and confirm the brake has a large enough bore for the .308cal to clear.
Beyond that, I'd ask when the cerakote was done, and if you had it done or bought it that way. It's possible theRe is a problem with the coating if it's gotten into the bore and made the surface uneven.
Finally, what is your zeroing process. What's your setup (rest/bags, etc.), where do you aim, what distance, and how much experience do you have with rifles which recoil at this level?
I highly doubt it's the pencil barrel. That might contribute to larger groups, but the lack of ability to zero isn't the barrel contour.