Wouldn't banning the breeding of any invasive animal work? Sure keep one as a pet if your into exotic pets, but you are responsible for making sure that snake dosnt reproduce.

Also allowing year round unrestricted hunting of these invasive pests would help.

People like guns and they love hunting. Some things they can only hunt at specific times....but if you tell them they could hunt as many as they want year round you would suddenly see a bunch of people figuring out how to hunt a snake with rifles or other weapons.