If it were me, I'd get a quality 165 grain or 180 grain bullet. I'd practice and know I was good out to 400 or 500 yards. 300 yards is a piece of cake, 400 takes a little practice and 500 takes a little more pratice. Finding a quality round that shoots good at 100 yards out of your gun, is a good start. Then use a ballistic chart to help you move out farther. A ballistic chart is no replacement for a little practice but it sure makes it easier and takes out a lot of the guess work.

I have always found that the bullet that shoots the best at 100 yards, shoots the best at 500 yards.

308 is plenty of good medicine for elk.