Berger 180 grainers 7mm, have BC greater than 7. Slick little bullets. To me, the .308 offers nothing in this arena.
For that matter and that distance, why not build a dedicated rig if money available. How about this: bedded in McMillan A5 stock, remington action trued up or after market action, heavy contour match barrel about 28 inches long plus or minus a brake, and 7mm STW or 7mm ultra mag or 300 win mag or 300 ultra mag. Badger bases and rings plus a leupold 8-25x50 tactical scope.
If money is an issue, get a remington 700 with a nikon monarch scope 4-16 in 7 mag.
Either way give it lots of practice. When you start shooting at distance, it makes you realize that the cerebral game of which is better cartridge wise is not that important, because you realize until you practice more you won't be shooting at distance at live game.