Long Range Shooting
I see that you live in Austin. You might check with the Camp Bullis military base north of San Antonio. I've shot at 1,000 yard matches there back in the 70s. I'm pretty sure they still host matches there where civilians can shoot.
Even just watching one of the matches should give you a good idea of what works well and what kind of rifle you should get for such shooting. These are pretty specialized rifles, but not so much so that they can't be used for hunting or other shooting. They are shot from the prone position with sling, many with aperture sights. No sandbags or bipods are permisable although handicapped shooters can use such aids.
I've only shot the 7.62 NATO and the 300 Win Mag at 1,000 yards in military rifles (M-14NM, M-24 SWS and the Mk 13 SWS). Believe it or not, the 7.62 does pretty well way out there and barrel life is significantly better than with the hotter rounds like 6.5/284.
Do a Google for the Texas State Shooting Association too. They should be able to get you oriented to a long range match or two.
The standard National Match course goes from 200, 300 to 500 or 600 yards. You might look into that option. Most shooters use their NM rifles for the long range 800, 900 and 1000 yard matches.