Document the condition of your fence, now. Then again after each damage.
Call Animal Control (or whatever it's called in your area) for each and every incident. Get a copy of each incident report.
Spray affected areas with OC Pepper spray, ideally when the dog is around, especially while damaging fence. Get the bear deterrent sprays, lots of capacity there. Dogs are 1000 times more sensitive than humans. It's a temporary solution, but over time may (or may not) condition the dog to the fence on your side.
Chicken wire, metal reinforcement. If they turn to digging instead, pour concrete, not a lot is needed to deter digging, an two or three inches deep along affected areas. Do not build a man-trap or dog-trap, even on your property it will lead you to big legal bills.
You're absolutely right about shooting, avoid if possible as people think of dogs as children, but if someone's life is on the line...
Consider this. Pit Bulls (most of them, anyway) have the self-preservation instinct bred out of them. So when they bite, they often stay clamped down even when injured. This was a necessary part of the sport they were bred for, bull-baiting (bringing down bulls). As such, once they clamp down on a human, they have to be shot off, cut off, or unconscious to be removed.
Be prepared.