Migp, welcome to MoveToNZ.
I quite sympathise with you when you say you're uncertain about the whole immigration process. It's a very confusing one and the NZIS site is like the black hole, you fall in and can't find the way back out again.
It's OK if you fit into all the slots neatly, but if you don't it can be a problem trying to make a round peg fit into a square hole.
Many people who can't find another way into NZ do go on Visit Visas and then look for work when they're there, as you've suggested. When a suitable job is found, you can apply for Work Permits which allow you up to 3 years in NZ. During this time you can gain NZ work experience which can be important when totting up points. This method is fraught with risks and similar to stepping off a cliff, but many have done it and succeeded. That's not to say some also have failed for a variety of reasons.
There is a debate currently going on here with conflicting information regarding whether a degree is vital for a PR application or not. Perhaps you've already read it. The NZIS site and, indeed, information coming from their offices is very ambiguous and confusing. I don't suppose your partner is an admin manager, as that is listed by NZIS? Have you double-checked that your job title as Manager isn't on the list, too? NZIS seem big on bringing in manager-type people.
I don't see South Africa on the list of countries that are entitled to apply for a Working Holiday Visa, so that doesn't appear to be an option. That would have meant, if you're under 30, you could apply for one, which, again, would entitle you to enter NZ for long enough to find a job and then apply for a WP.
So, short of being an investor in NZ (requiring an investment of $1m) or starting your own business (requiring previous experience of same in SA), it looks like you're left with the tourist way in, I'm afraid.
Sorry, I'm not being much help, despite being sympathetic to your dilemma. I hope someone else can add more helpful information.
