Chickens are not native anywhere in the US. Chickens have been domesticated from other countries. Even if a breed were developped in a certain area they had to come from birds brought from other countries. Kinda like there are horse breeds that started in Iowa and there are wild mustangs in the southwest but horses are not native. The mustangs are mostly from spanish stock mixed later with other breeds from other countries. Most of our livestock and pets are not native to this country. Alot of those that are could not be kept in the city. Are you going to get permission to keep a buffalo because they are native, you aren't breeding them, and you are keeping it as a pet instead of for food? All the arguments I've seen so far go both ways. Your argument that the laws exclude other pets also would allow the keeping of many other animals that definitely would not get along in someone's yard. I don't think it will work for that reason.
I think your better off getting together some people who want to keep chickens, maybe even some people from outside the city limits who do keep chickens, bring up laws in other cities that do allow chickens and talk about how well it has worked there. That's how most people have changed the mind of their city council. They show how it has been done elsewhere and worked and that a few chickens do not make anymore mess or noise than a dog barking and pooping all over someone's lawn. It would be better long term to get them to change the law or add a specific chicken section than to just try to slip through the cracks for now.
