Hi Jonathon
To get a variation of conditions you would need to apply at the Wellington branch of NZIS on Willis St - full contact details at
www.immigration.govt.nz/wellington
I'm by no means an expert, but I honestly don't think your chances are good. Whilst the partner of a postgrad student is generally entitled to a work visa, being in such a situation is not included in the criteria to be entitled to work on a student visa. They don't tend to be particularly flexible about such things, even where it would make logical sense, as here - hough don't let that stop you trying. I'm sorry I couldn't give you better news.