Grey Ghost Precision Barrel Nut Fitment

[JsnSanko]

On a Proof CF AR-10 barrel. Barrel was thermally fit to the upper. ID of barrel nut is 1.170ish, and OD of Proof CF 6.5CM Barrel Shank is 1.200. I have the GGP 18” hand guard that barrel came with?

Suggestions? Thinking of finding a machine shop to take .004 out of barrel nut. Want a precision rig here. Or is there a different barrel nut that would be compatible.

Rest of build is Magpul PRS Gen 3, JP SCS, SSE-E Trigger, Aero BCG, Fat Bastard Gen 3 Brake, and Nightforce NX8 2.5-20 scope.

Thanks for the help.