Kirby we are just jealous. I want a 338 AM but don't have the cash to pony up for it.
You are correct in your statement about things getting difficult with the 300 win mag past 1000. I have done a fair amount of rock shooting and clay pigeons at that range and my rifle shoots very accurately that far but in the areas I shoot there are a lot of canyons between the gun and the target. On days that are calm, which there are very few, we shoot clay pigeons. On days that are not I am lucky to hit the hill. Each canyon has a different wind blowing a different direction and speed. Sort of a unique place, coastal fog on one side and very hot heated valley on the other.
In a hunting situation I would not attempt a shot past my comfortable range for the conditions. Some days that would be 500, some it would be 1000. With the 338 AM that range would be bumped way up, I would expect the low limit to be somewhere around 8 or 900.
I have not had the pleasure to shoot one of your rifles but from what I have read and heard from people they are super accurate and a joy to shoot. If I had one I am sure I would shoot everything with it like the original poster.