at the long range matches they are shooting 4-6 inch 10 shot groups at 1000yds regulaly,so its not a fluke, the winning groups are smaller than that and 800fpe to 1000fpe is easily abtained at 1000yds with these rifles.when i hunted long range i used a rem. 7mm mag with a 162gr bullet at 3000-3100fps that weighted 16lbs with a 6.5x20 leupold target scope. these rifles have more fpe and fps that a win 30-30 at 150- 200yds.
Sure, on a surveyed range, with wind flags, a spotting scope to read the mirage and a couple of sighting shots.
Even with a 338 Lapua (250 gr @ 3000 fps) if you take a poke at a deer you think is 1000 yards away and it is really 980 he will be off in elevation by over a foot.
If the 5 mile an hour quartering wind you estimated is really 7 mph from 55º, you windage at 1K yards goes up from 23 inches to 36in. If you are lucky you miss, if not you end up with a gut-shot cripple that will starve to death, because you will have a hard time even finding the spot where the deer was standing after hiking the half mile from where you shot.
Shooting a game animal from that distance is unethical. You may try to justify it because some assclown did it and you saw the video on youtube is meaningless, because it was unethical when he did it too.
Rationalize it all you want, it is still unethical.
You want to shoot an animal that far away, go hunt Prairie dogs. Pretty much any hit with a rifle capable of getting out that far will be dramatically fatal to a small rodent.