Freedom Center USA near Lebanon, Missouri.
17470 Hwy HH, Lebanon, Mo 65536 (417)718-2597.
25 shooter-wide, 1000 yard range. Retail sales area, with gunsmithing shop. $300/yr membership fee.
Also, I think there is a private range in Billings, Missouri, another one near Fellows lake just north of Springfield (Springfield Rod & Gun Club?). No idea the max distance of these ranges are.
Big Piney Sportsman's Club in Houston, Missouri (South Central Mo/Texas county) is a great facility with 800 yard range, covered shooting positions, pistol ranges, 3 gun range, 200 yd zero range, trap & skeet ranges, and sporting clay ranges. $100/yr membership fee. BPSC hosts many, many weekend shooting matches, such as PRS/Missouri Steel Tactical (MOST), as well as a 2x/yr AK tactical shoot called Kalashni-Con.
Also, you are very near to OFASTS (Ozarks Full Auto Trade Show & Shoot) located in Wyandotte, Oklahoma. This is just off Hwy 60 just inside Oklahoma, a few miles past the Missouri state line. Check it out.
Also, not 1000 yards by any means, but Missouri Department of Conservation has quite a few gun ranges throughout the state. Usually they are 100 yard & 25 yard rifle/shotgun/pistol ranges. They provide target backstop & paper targets. They are un-manned public ranges open from dawn to dusk, and anybody can go shoot... so beware... But they are very good resources for those who like to pick up range brass. Two Cons. dept. ranges local to Springfield are: Busiek (located on hwy 65 between Springfield & Branson) and Pleasant Hope (located 20 miles north of Springfield on Hwy H).