You could easily rechamber to .243 AI, but the barrel would need to be set back enough so that the bolt won't close on the Go headspace gauge.

One other comment: although I know there a many shooters who have gotten good accuracy out of the 6MM Remington, I feel like the average .243 Win will group better than the average 6MM Rem. Same deal with the 30/06 and .308 Winchester. Or the .300 Winchester compared to the .300 Weatherby. Individual rifles vary, but if you took an average . . . . . .243 Winchester comes out ahead.