I think the problem with the .308 would not be on the insert or chamber themselves. It's more what the back pressure from the high intensity round would do to the action. Head area of the .308 is approximately 1/3 that of the 12ga, but the pressure of the .308 is on the order of 5 times that of the 12. You would have a lot more back thrust against the standing breech.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra