Thats a real stretch for a .308. I’ve shot at man-sized steel targets at 1000 meters with a .308. With NO wind, and pre-determined ballistics for the load you are using, a very good,repeatable adjustment scope,AND a precise lazer range finder , its not too difficult. Add another 500 meters, any wind at all, it would become VERY difficult with a .308. One of the better cartridges for this would be the .416 Chey Tac. It is probably a little superior to the .50 BMG for anti-personnel work. ,although it is based on the same sized case.
The .338 Lapua is sort of between the 30 calibers and the big “50” in both range, and weight. It can be made in a lighter package than those guns that are based on the 50BMG, and still deliver the goods at well past 1000 meters.
as does the .416 Barrett...