Re: Max effective range for a .308
308, plenty for elk. 168 AMAX, not so much. Take it from a guy who has extensive knowledge about the 308, its ballistic capabilities and AMAXs in 308s.
My top choice load for the 308 for elk is hands down the 200 grain Sierra Game King. It has a good BC, good sectional density and its velocity for expansion zone is perfect for the 308. Fired out of a large magnum it wont hold up very well on elk for close up shots but at 308 velocities its perfect. That said, it will also expand at 1500'/sec which with its good BC at elk altitudes will get you way out there. More energy is better but if you can take a double lung broadside shot and have 1500'/sec or more, I would not hesitate.
At 6500' ASL and 35 degrees F. and 2500 FPS at the muzzle, 1500'/sec comes at 925 yards with 1000 foot pounds of energy. If you go with the 1500 foot pound rule, it gets you to 575 yards. Most will argue that this is where you should stop. Either way, iit is a legitimate 600 yard elk load.
2500'/sec is very doable in a 308 with a 24" barrel or longer. With the right powder I have milked 2650 in a 26" but it is a high pressure load and it takes powder that isnt known as being as temp stable as some of the H powders. 2500-2550 is a realistic number for the 308 and the 200SGK.
Long range shooting is a process that ends with a result. Once you start to focus on the result (how bad your last shot was, how big the group is going to be, what your buck will score, what your match score is, what place you are in...) then you loose the capacity to focus on the process.