Aweful situation to be in with your neighbor.
Before I got chickens I went to the town office to make sure it was OK, and ask what to do if the neighbors should complain. At the town office they looked at the property maps and said I was in the agriculture zone so I could have whatever I wanted for animals. I only own two acres so ask if that made a difference? They told me absolutely not, as long as I was in the agriculture zone I could raise elephants if I wanted to. Mentioned I was worried about the neighbors complaining about crowing roosters. They looked at the map to see who lived nearest where I was going to put the coop. I told them the people closest to the coop were renters. I was told that since I owned my property that my happiness came first and if they complained then tell them to rent in town.
Fortunately my neighbors have never complained in the almost 12 years I have kept poultry here. At times I've had up to 20 roosters crowing at all hours of the day and night. My coop is right on the property line. As a courtesy I do try to keep the rooster population down to one rooster.
I am sure my neighbors at times hate the sounds of roosters crowing and chickens cackling but they've never said anything. Of course, I have never said anything to them either about their constant preaching ans hymn singing and let me tell you there are times when I am in my yard that all I hear is preaching and hymn singing for hours and hours at a time. I just roll my eyes and start singing trampy songs with swear words LOLOL Joking! I actually love one of the daughters voices and oftentimes sit in the yard swing and listen to her sing.
OK, on to your problem. I would get a security camera and security geeese. The geese are great because they'll honk loudly if they hear or see anything at all. They can also be quite protective of their property.
Good luck. I hope it all works out in your favor.