There's no 1 way to prove you two are living together as each situation is always different hence why the guidelines around what evidence is acceptable for proving this is very vague...
First of all don't assume anything, don't assume online shopping holds no power with INZ every little thing counts. So do online shopping, put her on your bills, do absolutely everything you can to get as much mail as possible addressed to the both of you, doesn't matter if it's a joint letter, or has her name or your name alone, it all shows you are at this address. Sign up to reward cards, get a library card, do absolutely everything you can think of to get mail.
As far as more formal options other than the bills, you don't really have any, that I can think of anyway, unless opening a bank account is possible? Explain in your cover letter that she has been in NZ on a visitor visa and has not been able to get access to X,Y,Z.....
Get neighbours who see you both daily to write letters, friends to write confirming you have been living together.
I know it's frustrating and stressful I was in a similar situation to you just a few weeks ago but you will be fine as long as you just think outside the box a little bit and ensure you're getting as much mail as possible...