I use a 165 gr Sierra KG HPBT in mine up to 750 yards, but after that I go up in power to my 300 Ultra Mag or .30/378 Wby both using the Nosler 200 gr Accubond. Before either of these were mainstream cartridges, I used a 180 gr Hornady in one of my .300 Wbys. In order to shoot game at those distances you will need to do quite a bit of practice and be very peculiar with your shots. Very few places afford enough room for those types of shots. I my uncle spent many hours with me starting when I was about 10 until I was in college teaching me how to shoot distance targets. I learned many good techniques from him.

From 40 years experience, I can tell you to weight sort all your brass, bullets, weigh all of your powder charges. True up your case necks, flash holes, primer pockets. When I shoot that far I use once fired cases neck sized within .005" of the shoulder, so they are tight in the chamber. I seat my bullets .0005" off the lands, I check each one for function to see that all chamber. I check all loaded rounds for run out.

I can tell you that it is very gratifying to take down an animal at a 1000 yards, but most of mine I shoot at that distance are hogs. Even if a hog runs off for a couple of hundred yards after being shot, that is no big deal. A wounded deer or an elk can cover a lot more distance than that. That brings up the ethical question are you really good to shoot game that far? If you can honestly answer yes, then by all means do so. If you are shooting targets or wrecked cars, send them down range!
Good shooting,
Marcus.