Rural Wifi

Since I don't know what things are like in New Zealand all I can do is tell my story. I lived in a rural area of California. Didn't have DSL or Cable available, could have used Satellite but didn't for the same reason as yours. If you have cell phone service in your area, then check with those providers about using a Jetpack. It's just a little WiFi amplifier. It has a phone number assigned to it and gives you up to 4G service. They start at 10gigs of Data per month but if you need more, then you can get your plan adjusted. These little Jetpacks can be taken and used anywhere that you can receive a signal. We have a place called Best Buy. It's an electronic and appliance department store and has a cellphone department with access to three different providers and they can check on a computer to show what cell phone service has the strongest signal in your area. I had Sprint, AT&T and Verison as option, I used Verison happened to be the stronger signal and the better plan.

This looks good...

"It's all about what you are willing to spend.

You could install your own point-to-point microwave specifically designed for what you want to do.
A pair of Ubiquiti airMAX Nanobridge M units will do what you want. They can use TDMA in a point-to-point situation with an advertised range of 20 km. I use 4 of these and my longest hop is 41 km (26 miles) with perfect results. I use the larger 16 inch dishes. In the TDMA mode, there is near-zero latency and nobody is going to leech off of you either.
They are PoE powered (injector is included) and setup is performed using a built-in webpage type interface similar to any router. This is carrier-class equipment.
Cost: about U.S. $80.00 each on Ebay. Search for "Nanobridge M."
The Ubiquiti site is HERE. Click on the Nanobridge M picture-link under the words "Airmax antennas."
They are available in 4 versions: 900 Mhz, 2.4 Ghz, 3 Ghz, and 5 Ghz. and no license is required in most countries.
It is also possible to use just one unit as a standard Wifi receiver, AP, or bridge."

http://www.tomshardware.com/forum/39902-43-long-range-miles-directional-wifi-signal-boosting

https://www.ubnt.com/products/#broadband