Then the heaviest bullet you can push as fast/accurately/safely as possible will give you best for beyond 500 yards. As components are tough to get, I would start with at least the 185s and go up from there. 215s are great, if you can find them, but they are not easy to shoot in a light hunting rifle. I don't think it is a matter of the bullet killing an animal if placed correctly way down range, it is more of the ability to to get it into the vitals correctly. 308 starts to fall apart about the 600 yard mark-conditions just don't favor the lower velocities. Targets yea, but how many shots does it take someone to be on at 800, 1000, etc. consistently/predictably. 500, 600, 800, 1000 yards on a groomed range with wind flags is significantly easier to get "hits" on target than real world hunting conditions. With a 215gr Berger out of my rifle at about 600 yards a 10 MPH wind moves it about 3.5 MOA, that is a pretty big wind to call properly/consistently.
I love the 308, learned long range on it, but long range hunter probably would not be my first choice at least not animals...
That is why stacking the odds with faster is why alot of folks go big...and it is pretty fun...