Not sure about NZ, but radio stations in the US regularly rebroadcast into areas using different licensed frequencies. You must be licensed of course to do that, and it would probably require radio station permissions or oversight to avoid copyright issues of reproducing/rebroadcasting copyright material. Small transmitters are available for pirate or licensed low-power FM use.
As far as streaming, you can put a windows XP box online with winamp with a radio hooked up to the line-in. This will let you stream from a different location via browser or winamp.
Our approach has been that what the authorities don't know doesn't worry them. Anyway the alternative to this scheme in our neck-of-the-woods is no reception at all. All we'd be doing is making something available to us which is available for free to 80% or more of the population who live in zoos - sorry, cities.
Your streaming idea sounds like the answer, save that having to have a Windows box up at the AP wouldn't be my first choice. I'm guessing you can get a PCI card which will take the raw FM signal and convert it into 'radio', as you can for Digital Satellite TV, but it would be a big power draw and mountaintops are not very PC-friendly places. If it could be done with a laptop running Linux it becomes more reasonable, but that probably rules out the PCI card approach.
Still, food for thought. Thanks.