I like the 308 and have loads that I can poke out to 700 on CXP2 sized game (deer and antelope), that is with terminal velocity to provide at least 1000 ft lbs at point of impact.
For CXP3 type game, my ethical limit is 1500 ft lbs of energy.
So looking at a nice load like a 180 Nosler Accubond thats only 450Y.
I worked some numbers and if you can get a 208 VLD up to around 2575-2600 you can hit 1500 ft lbs at 550-600Y, not sure what that load will do do your primer pockets though.
If it were me, I would look at the 190 Nosler ABLR with its .640 BC, get that one up to 2600 FPS, for a range of 500Y. Anything beyond that you should really look at another rifle.