Did you contact the NRA's Whittington Center Range down in Raton? I've never shot there, don't know what they'll allow, but I've heard they do have a 1000 yd. range. It's a drive from CLSP, but not that bad. Only other bet is to go out and meet local ranchers and beg/kiss ass for permission to shoot on their land.
Myself, I'm too old and blind to even worry about 1000 yards, let alone 600! I look at the big targets on the 600 yd. line at BLGC and say "WTF", I can't even see that sumbitch.