My neighbor who lives on the corner has a nice flock of leghorns and a very nice coop. His run left a lot to be desired, a flimsy one layer of 3 ft chickenwire with no top. Mostly his chickens free range. Nobody in the neighborhood minded until they started going into the road. On our small street, we have five new teenaged drivers. One day after school, one of them almost got rearended as she was turning into our street. The chickens were scattered all over the road and she didn't want to run over them. The car behind her that was going straight was no doubt following her too closely and going too fast.
So as a result, Gabby's mom went to talk to the neighbor. He was very apologetic and we have not seen his flock in the road. He also added that should they get in the road again, he would rather lose a chicken than have an accident be caused by them.
The OP says the people they are dealing with are not nice, reasonable chicken owners. Since he says he has already talked to them and they do not keep their chickens home, I agree that he is within his rights to do whatever is necessary. I, for one, vote for a silent solution and love the idea of chicken fricasse.