The province of Alberta, Canada (more than twice the land area of New Zealand) is free of rats.
In their case, it was largely by stopping rats entering from the east (Saskatchewan) in the 1950's - there are natural barriers on the other three sides.
History: http://www1.agric.gov.ab.ca/$department/deptdocs.nsf/all/agd...
Still, NZ could be divided into areas that have natural barriers, and peninulas (plenty of them), and start intensive poisoning barriers in those areas, expanding towards the sea.
Doesn't need gene editing, which certainly has unknown risks.
