What is your barrel length and twist? If you are looking to go to 400yds, the high BC bullets are a great option.
I have had good results with the Amax at longer distances. While they are not recommended for hunting, they are an expanding bullet and I use them for distances between 400-700 yds due to their violent expansion. I have had quick clean kills with pass through at distances as far as +/-650yds. My go to load is 46.1grs Ramshot Tac, 178 Amax, FGMM Primer, Lapua brass, OAL 2.815, 2810fps. I would not use this bullet unless you are shooting at distances where your velocity will be reduced.
I use a 165GMX when I am expecting shorter shots 48gr CFE223, FGMM primers, Lapua brass, 2.810 OAL, 2920 fps
The nice thing about the .308 is it shoots most bullets rather well.
***Remember, start with lower charges and work your way up. These are loads I have used after careful testing