Believe it or not, the solution to the City's rat problem may come from an unexpected source........weasels.
https://www.dnr.illinois.gov/conservation/wildlife/Pages/LongTailedWeasel.aspx
Numerous sources say that when given a choice/chance, weasels will feed or rats and mice almost...
My suggestion is to abandon any notion of keeping roosters. On balance, the noise they make in an urban setting will cancel any benefit of protection from rats, which I doubt they do anyway. Work with your city folks......don't fight them. Be ruthless with fighting the rats.......at least the 4...