I'll just throw this out there because no one else has yet.
The big 338's with a modern designed quality muzzle break
. They have the power to take elk at 1000 IMO. According to the ballistic program, my 338 AX shooting the 300 grn Berger still has about 2700 ft.lbs energy and is traveling about 2000'/sec at 1000 yds.
I've shot the 338 Edge and more recently my 338 AX quite a few shots in one sitting. Neither rifle is extremely heavy, I'd guess they are around 13 lbs with heavy scopes installed (note to self, need to weigh it). The Edge wore one of Shawn Carlocks breaks, the AX wears one of Kirby Allens breaks. I am quite certain and would almost gaurantee that they both recoil less than a bone stock 7mm Magnum.
Sorry, I brought up cartridges that need to be handloaded, but I doubt there's much 338 factory ammo that is up to the challenge of 1000 yd accuracy/performance that we can get from the Edge and AX with handloads............338 RUM is a factory round and 338 Lapua can be bought pre-loaded too, but IMO the 338 RUM doesn't come with the best bullets for 1000 yd game shots............The Lapua ammo perhaps does, but the BC of the 338 RUM stuff I've seen is only around .5
I agree with others that 1000yds is no "walk in the park". A one shot kill at 1000 is beyond my ability
at this point, even with the ballistics and accuracy of these high dollar custom rifles
and top notch match grade ammo. Lots and Lots of practice is needed IMO.