Ok, my thoughts from having studied ecology and I have a cat. Also I haven't read this thread, it's too long.
The only way to really get rid of cats for the benefit of native fauna, is as part of an eradication of all pest mammals at the same time. Cats do help control rats and mice. If you remove cats other pests take their place. And Gareth Morgans figure of how many things cats kill, includes rats and mice.
The only places where I think an eradication of a large area would be Great Barrier Island and Stuart Island, which would be hugely expensive and take a very long time.