Why not stop using poison and just let some cats lose. My city ally has a healthy cat population most of which have been TNR'ed. The only rat I've ever seen was the severed heard of one that some kittens were devouring on the pavement.
Fast forward 5 years, you got yourself a healthy plague of feral cats - plus complaints from regular cat owners that the ferals pick fights with their cats. In addition introducing mass numbers of cats causes a rapid uptick in bird deaths (cats can eat islands virtually birdfree) and they're a considerable risk for accidents with vehicles or small kids.
Key West has an informal program of spay/neuter of feral cats. They also inoculate them and notch their ears. It stabilizes the population.