There's another alternative that gives you an incredible picture of the target that's within your budget, and that's a target camera.
https://www.longshotcameras.com/coll...ducts/marksman
https://www.shootingmadeeasy.com/bullseye-range-camera/
No mirage and the batteries last longer than you'll want to be at the range. I used one like these to shoot 1 mile and it was great.
{Edit: The links are OK, but the images violate the board policy on posting copyrighted material unless you got permission from the copyright holder. The links are OK.}