As a New Zealander, unfortunately, I fall into the category of cheap overseas contractor. With our weak dollar working for a US company is a good way to earn above average. We're still much more expensive than some of the cheaper countries. In fact we're currently working with a Vietnamese contractor. He is very good and much cheaper than a local hire.
Please don't go into remote work with this attitude.
We speak fluent English and if we get up early we have a great timezone overlap with the US. There's no reason to settle for NZ rates with a US company.