The Killdeer is a protected species, so shooting them (either in a preserve or anyplace else) is a violation of federal law unless you have a permit from the U.S. Fish and Wildlife Service.
It also would not solve your problem. The Killdeer are not nesting in your slide topper. It must be something else. Killdeer are almost exclusively ground nesters, although they have occasionally been known to nest on gravel roofs.
If I had to guess, I would think that the most likely culprit would be House Wrens. Check out the songs House Wren, Sounds, All About Birds - Cornell Lab of Ornithology
and see if you are hearing that.
What do the nests look like? What are they made of? Can you post a photo of a nest?