1000 is possible with a 308 but only with certain bullets. I think the big thing now is what ammo or reloading bullets can you find?
Here are a couple of loads
available at Midway that will do 1000 yards easily with very low drag bullets. But you will have to try different loads to see which one the rifle likes, and at the moment, there isn't much available, either loaded ammo or component bullets.
https://www.midwayusa.com/product/953728886
https://www.midwayusa.com/product/102335492