Just cannot believe what you are having to put up with.
I have a neighbor that will call the cops if a dog barks during the day. (mine were barking at a fox) We also have an ordinance about harassing animals behind a fence. She was seen harassing my dogs to keep them barking while waiting for the cops. I informed her of the ordinance and that I was putting up video cameras. Now she calls me at work 30 miles away to complain. I come home and check the bark collars and camera's. One bark should not constitute a call IMHO.
Where I live the ordinance states "as many as can be properly housed and cared for without causing a health hazard or nuisance". There is a stipulation of no roosters. I currently have 22 hens that are far noisier than my dogs. My mother lives farther inside town and I hear a roo every time I am over there. I guess no one is complaining about him.
When I lived in the country I had a bantam cochin roo that I could hear from 3 miles away at the stop sign by the highway. He had a distinct sing song sort of crow. Sure miss the little fella.
It is a shame some people feel the need to concern themselves with what goes on on the other side of the fence.
I feel your pain and hope for the best.