This may sound odd, but in spite of the numbers of gun people in this area, I doubt many have any interest in competitions. Most I know like to hunt. There's deer in season, birds in season, and then an abundance of pig and coyote hunting year around.
I think the range you speak of is The Abilene Gun Club. I don't know any particulars about it. A good many people who shoot a lot in the area have developed connections for locations on private property for rifle shooting and even some pistol shooting. A lot of folks use the Abilene Indoor Range and the one in Anson for short range needs. There is/was a long range rifle range toward Winters or near that if I recall. Check on the local website, "Abilene Area Guns", to check on that long range location.
Personally I have places on private property where I mainly do long range target shooting, and there are places where I coyote call and pig hunt...but they are not places I have control of or can share.