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NZ effectively requires a BSN. This is a bit strange as a BSN takes only 3 years in NZ and an ADN here takes three and a half years counting all the required coursework at normal speed. In addition, their degree is structured like a diploma program when it comes to clinical rotations inside the degree requirements - it is unlikely for American graduates to have the required time in each specialty. Which is why you effectively need a BSN to cover clinical deficiencies (or a long career).
Once you are licensed (you don't need an agency to help, but it will take some time), I would personally recommend traveling to NZ and exploring. It is inexpensive once you get past the plane fare. NZ is a rare country that allows you to travel on a visitor's visa, look for work, and stay to work without leaving the country. Then you can better explore the best option for you.