Shell, I totally have to agree with you about the NZIS site. If I got paid for all the hours I've trawled through it fruitlessly, I'd be well off. I absolutely loathe the site as it's geared to sending you in a complete circle and back to where you started without the answer you were looking for. There's so many promising-looking links on there, but when you click on them they just don't say anything, just a lot of meaningless hot air that's already been repeated elsewhere. I'm sure the NZIS site is one of the major causes of my increasingly frequent hot flushes (or flashes, to you).
Anyway, if you take a look on
here and put the number 4 in the page box at the bottom, then scroll down a bit until you see a list starting, you can see that Adminstration Manager (and I assume this is similar to your job title) is there. The title of the document is Occupation and Region of Employment for approved SMC and General Skills Principal Applicants so that, to me, sounds like you could get in with that.
You only need a minimum of 100 points to be able to submit your EOI. It's 140 points for automatic selection but that MAY be coming down at some point. They change their minds like I change my underwear. If I were you, I'd try to gather as much proof together of your work experience as that counts for quite a bit as well.
If this doesn't answer your question, let me know and I'll go on looking.