I would look into any farms/foodrights type organizations. They can fall all over the spectrum politically. (Far left, far right, moderate)
NY must have some groups like this. There might be $ for litigation/lobbying. They may also have suggestions on how to skirt the rules or something we don’t even know about.
Calling your federal and state reps/congressman may not help, but all the ones I’ve worked for before I settled into my career job, track constituent inquires by type and number. If they get 10,000 inquiries about backyard chickens, you might see some action. Or if the city council gets inquiry letters from a few congressman, they may compromise with you.
I don’t know what the laws are in NY...but record every interaction you have with any figure of authority.
Or you could do what I did a few times as a young man, when someone tried to bully me under cover of authority.....bully them back. Show up at their house. Show up at their job or office. Show up at their kids soccer game. Call their parents - this one actually worked the best.
Luckily it worked out and I am a much more mellow middle aged man. And you look like a nicer person than me

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