That's such a strange requirement. What brilliant politician came up with that one? Seriously - who writes code down to 1" inch beneath a small outbuilding? It's a good thing they removed that requirement. That would have been silly and difficult to control.
Sorry about your rooster.
Their rules sound very close to Auburn's rules. What are the set-backs? Ours is 15 feet. That's how the city controls chickens in what I term the "McMansion" lots (really big houses on 5,000 sq. foot lots). There's not enough room to accommodate set-backs so those houses can't have them.
In Auburn, we have to have a 6,000 square foot lot before we can get 3 birds. The rest is the same as your area.
In Auburn, chickens have been illegal for so many years, getting neighbors on board with the idea has not been easy. I still chat friendly with my neighbors, but I can tell they don't like them. Only 1 neighbor, a German lady, was excited to see them. Most of the neighbors are nice about it (I got criticized by one gal, but, whatever - I can't seem to do anything right by her anyway). I can tell the other neighbors really aren't comfortable with it. I could have 6 on my lot, but we started out with 3 for that very reason. I'm keeping them pristinely clean - hoping to change whatever preconceived ideas that they have about them. Why is it that having a chicken as a pet seems to be such a scary thing to people? I'd rather meet someones chicken than the many pit bulls we have in our neighborhood.