I believe that’s already been done. Sig is selling the .277 Fury (civilian name of the same round) in a conventional brass case, naturally, it is loaded to significantly lower pressures. Much more in line with a 7.62X 51.
Full pressure round:
https://www.sigsauer.com/accubond-277-sig-fury-hybrid.html
Conventional brass case:
https://www.sigsauer.com/elite-ball-fmj-277-sig-fury.html
Sig has offered the rifle for sale, but it ain’t cheap. I think it was a bit over $3000 just for the rifle, and if you wanted to suppressor, add another grand. I don’t see any for sale in the new caliber right now, but it is this platform, currently available in 7.62x51:
https://www.sigsauer.com/spear.html
Nobody’s talking too much about the details of the optic system, which was contracted out to Vortex. From the pictures, you can see a low, powered variable optic with a red dot on top. It looks like a pretty capable set up, and there are rumor to be some features like automatic ranging, and management of round count, among others.