Here in Austin the city rules can be made more restrictive by Home Owner's Association (HOA) rules. Which sounds like what you are stuck with.
The city rules say yes to hens kept in an enclosure at least 50' from a neighbor's house. But if you live within an HOA, then their rules can dictate no hens at all. Then their rules apply to your property.
Read through all of the covenants and rules closely, just to make sure. But it sounds like you have already started getting rid of your birds.