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I killed an antelope many years ago with AK variant. Range: approxiamtely 100 yds, two shots, First shot broke it's spine, second shot through the heart.
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That is archery range, not rifle range.
The most recent world record at 1K for a 10 shot group was set at Williamsport Pa. using a 300 WSM and Berger 210s. Group size was under 3 inches. That is only relevant to say that the 300 WSM is an accurate cartridge that competes favorable with the 300 Win Mag. Both cartridges have reasonable throat life. Two of the three people I know who have killed elk at ranges past 2K used to compete at Williamsport.
Bawden, before he designed his 338, used a 300 Win Mag and Nosler 180 ABs to kill two or three elk at ranges beyond 800 yards.
I do not have any personal experience with either cartridge but I know Bawden and most of his work was done with witnesses present so there is not much doubt about whether he actually did the things he said.
I will just remind you that you are on a forum dedicated to military skills and that is not the same as hunting skills. A military chamber in a rifle is a lot different than a specialized long range hunting rifle. All of my chambers are tight but not to the extent of needing to neck turn. Basically what I specify is minimum SAAMI. The throat is where one must make decisions and then live with the results. If one is going to shoot long high sectional density VLDs then the throat is cut so that the bullet is not seated down into the case body occupying space that is needed for powder. This then means the rifle may not shoot shorter bullets very well nor factory cartridges unless you can find ones that jump. It also may cause you grief in that the bullet will not longer fit into your magazine and then you may need to get specialized bottom metal. One way to get around this is to use a long action for a short action cartridge.
There is no disadvantage to using a single shot action for a long range rifle being as travel time is going to be long and if you miss there is a need to stop and think about what you did wrong so you are seldom in a hurry to make a second shot.
Loading manuals and factory ammo are designed for factory type rifles. Most of us who use 28-34 inch barrels for hunting use really slow powders which provide for very good burn in the long barrels and give us extra velocity.
None of this is to say a person cannot use a commercially available sporter weight rifle to kill elk at 1K but the odds of doing so get magnified. Lots of people kill elk out to 600 yards but that is where the average person will not practice nor spend the money for quality optics and quality parts so very few will ever make it beyond that point. For example, my spotting scope costs about $1K, my binoculars cost over $1K, my rangefinder costs right at $1K. So I'm into the sport for $3K and haven't even talked about the rifle.