Will you be loading your own ammo or buying factory ammo? If you are concerned about resizing the 338 Lapua to a .308 or 7mm neck It's relatively easy to that. but you will need custom dies for it. If you want only something you can get factroy ammo for, I would go with the 338 Lapua and you can send me all your used brass
For 1000 yd shooting you want a cartridge that can fore a high BC bullet at high velocity for downrange effectiveness. My criteria would be that the bullet has enough velocity to open and expand and enough momentum to fully penetrate. Depending on construction and size of the bullet you need a velocity somewhere in the range of 1500 - 1800 fps or higher. Your selection of factory loaded ammo that can do that will be limited and expensive.
Here is a list of standard factory cartrides that can shoot bullets to 1000 yds and effectively kill caribou and reigndeer.
7mm Wthby Mag
300 Wthby Mag
30-378 Wthby Mag
338 WM (marginal performance at 1000 yds)
340 Wthby Mag
338-378 Wthby Mag