Are you serious? They wouldn't tell you to shoot them? In Ohio at least over there that's the first thing they would tell you to do!! My parents neighbors had 2 german shepherd mix dogs for several years, they are not nice dogs period, they tried to attack our dog I grew up with they have tried to cross the property to get Shaianne, and when we raised sheep they tried to get to them, and they have stalked my dad out in his shed, he heard growling and turned around and there they were sneaking up on him, and they dog warden at the time told him, "Shoot them and bury them if they come across your property again"
He never had to do that, they stopped crossing the property line, and recently one died. Now I know that even if a dog is mean to people and animals, the person still loves them just as much as those of us with nice dogs. You can tell the dogs adored their owners even from across the yard, even tho I couldn't stand the dogs. I think that's wild that they wouldn't tell you to dispose of them. Here in this area of OH if the dog warden told the people to try relocate them, I think they would be the laughing stock of the county and the people would illegally shoot them anyway.
Good luck, this is obviously a national problem.