Persephone

This is very poor advice. NZIS do not accept marriage as the sole reason to issue residency. In fact they view it as little more than a supporting piece of evidence that you are in a relationship. To gain residency via partnership you must have lived together for at least 12 months, married or not. Getting married will not help your situation at all and could be detrimental.
Dolph, I do get the impression that you know that but it did need clarifying in case others read this!

As to how you can live in NZ, tricky one. Could she move to the UK? What are your longterm plans as obviously you cannot commute this far indefinitely? Personally I couldn't do it for very long, someone mentioned going to the USA and Singapore regularly-that I could do but NZ-UK is getting on for double the journey time.
Coming over as a visitor could prove problematic over time.
There is no obvious easy answer to this.

I think Simonsi's suggestion of an immigration agent or lawyer is a very good idea and normally I wouldn't recommend one. You may as well see what the Auckland office say when you go in but I suspect they will just tell you what is on the website. Yours is an unusual and difficult situation.
I cannot help with the issue of tax residency either so you need to contact someone who knows the rules for both NZ and the UK.

If you do somehow manage to get residency there are other ways of gaining a permanent resident visa than by merely being in NZ for a certain number of days. This is looking way too far into the future though. You need to get the immediate 'is this possible?' question answered first.

Anyway, good luck and please come back and tell us what's happening
P