In the 1980's, we had a "big gun" hunt for predators. People that had long quit deer and elk hunting, in order to hunt just predators would bring out their old deer and elk rifles. The 308 was great for varmints in that the 110g HP with H322 would just about cut a coyote in half, 125's(deer bullet) at 3200 with Win 748 was super accurate(check the nosler manual), and the speer TNT with 748 shot bug hole groups.
Now, these "big gun" hunts were for humane kills, they were not for collecting fur hunts, well, the fur did fly.
308 TnT means that a coyote gets shot about in half, terribly accurate enough for head shots at 200 yards with a Rem 700 Varmint.
Let's see, minimizing fur damage with a 308, hummmmmm........ maybe shoot the end of his nose off and break his neck....or maybe shoot the very top of his head off...these TNT bullets with 748 are accurate enough to do just that!
Good luck!