That makes my first idea a lot less practical.
Being able to get a clear, stable shot at something 1000 yards away is going to be on the upper end of the difficulty scale, without getting rather expensive.
Without getting too crazy, you can find 200mm C/CS lenses fairly cheap ($150ish). That would cover you out to about 300 yards (giving an HFOV of ~20ft wide).
I would mount 3 fixed analog cameras, 1 covering 0-50 yards, 1 covering 50-100 yards, and 1 covering 100-300 yards. Using 55mm,100mm and,200mm lenses respectively. Find a simple monitor with 3 inputs, or a 3 or 4 input switcher and wire it up. This would likely be cheaper than a PTZ setup, and less prone to breakdowns. Plus, it would be faster/easier for the shooters to control.
IME, a scope is going to provide MUCH better detail for the 250 yard + ranges, and is going to be an absolute requirement on the rifle at those ranges anyway. Shorter distances (and 300 yards is getting pretty long) you have a higher chance of people using low power scopes and/or iron sights, where a "close up" view of the target could be more valuable.
If it was indoors I was going to suggest placing cameras down the range, so that you could stay within ~200 yards of the target. There are ways to do that in an outdoor range as well, but it'll most likely require the cameras to be mounted on ground poles, instead of hung from a ceiling, and you'd have to do a little more to deal with bullet proofing them, and it could get in the way of turf maintenance.