Of the two you mentioned, 6.8 or .300 BO I would go with the 6.8. I know there is a lot of discussion on the differences between the two but when it comes to down range the 6.8 has the advantage and since you don't plan on a suppressor why not get the down range advantageous. On top of that, do you reload, if so the 6.8 would be a loaders dream.

Saying that, if in the 1960's the US gov't would have used their head the M14 would have been made in .243 Win, the FAL in .243 Win, or even the AR10 in .243 Win. The best of balance, ballistics, and recoil. But what could have been is not.

The way I look at it is if I can't do it with a 5.56mm then I move up to a 7.62x51mm and take care of it. If you need bigger than that, well get a lever gun in .45-70!