Scope - The longest confirmed sniper kill is 2430 m using a NF 5.5-22x50. Depending on what level of resolution you are looking for for targeting you could get higher magnification, but I have the 5.5-22 and can easily focus on small rocks, less than 6 inches, to 1500 yds using the 5.5x setting.
Cartridge - 338 AM. This is the largest 338 cal cartridge that I am aware of and is quite powerful. It's based on the 408 Chey Tac. You could step up to a Chey Tac, Barret or 50 BMG if you were looking for more than a sporter. But Kirby's sporter is no ordinary sporter.
Bullet - The GS SP 295, assuming your shooting is recreational and not live game other than varmints. It has an average BC of about 1 donw to about 2000 fps then falls off to about .76 before going transonic. You should easily be able to get 3500 fps with this bullet out of a 338 AM Raptor which should get you to about 3000 yds of suoersonic flight at sea level.
What ever cartridge yo choose, the GS SP's are very good choice for extreme LR.
Back in the mid 90's I did some work with a 375-50 BMG IMP. We had some bullets around 350 grains with a BC over 1. I can't remember which ones we were using for sure. We were making hits at 2-3 kilometers with it. I know we were pushing them over 3500 fps. I would have to go back and find all that data. I know they did well on the windy plains east of colorado springs where we tested it. I know GS makes some 375 bullets now with a BC over 1. I just remember it was fun to shoot that far and expect to hit something.
I have seen those videos before and they are some great marketing footage
Other than precision and accuracy, there are only two things that matter in LR shooting. BC and and velocity, in that order.
I did a little searching and found this article on the sniper country web site on the 408 Cheytac. It was a little surprising because it turned out to be a little less of a performer than I thought.
The bullet they are using has a BC of .9 and an MV of 2900. When you compare that to the GS SP 295 with a BC of 1 and MV 3500, there is no contest. The 338 AM shooting a 295 GS SP will leave the Cheytac waaaay behind. And I would wager that Kirby could cut the group size way down with his Raptor.