Pass legislation that creates high mandatory minimum fines for dog attacks on postal workers, and require that home insurers are responsible to pay. Allow and encourage communities to pass ordinances that require home insurance for owners of certain breeds. Require breeders to receive certification that buyers have notified their insurer of the purchase of a dog (regardless of whether it's covered).
As soon as there's a financial disincentive to own one of these dogs, the number of owners will drop off dramatically. The first few years will be tough as many people give up their animals, but the are dogs that should never have been bred in the first place. It's heartbreaking but necessary, especially when you look at the consequences of unchecked ownership of dangerous dog breeds.
Edit: Really curious why y'all are downvoting. You don't agree that dangerous dogs are dangerous? Or that you should be financially responsible for the risks associated with your animals? Really, what's the disagreement?