Dawn, I take it, by saying your stuff will have to remain in the UK until you are legit, means that you’re aware that, if you sent it before that time that you’d have to pay 12.5% GST on it when it arrives in NZ?  Those with PR or WP for over 12 months can bring their possessions in without being charged GST.  

We sent 13 boxes of household items from the UK to Oman the last time we were there and it cost us about £500 (doesn’t help much when you’re going to NZ, but gives you some idea of cost).  That was door to door.  We used a shipper and it was reasonably straight forward.  

You have several options for sending things:

part load in a container – you share a container with either a company or another person

palleting where they bung all your boxes onto a pallet and shrink wrap them then stick them on a plane or stuff them into a container as a part load.

sending it excess baggage – very expensive but speedy as it probably flies on the same plane with you.

sending it unaccompanied baggage – not quite so expensive but still reasonably speedy.  It could be on a different plane to you and might arrive a few days after you.

I don’t know how you’d stand with GST, using the last 2 options as your stuff would be arriving with you or shortly afterwards.  As you know, it could be very awkward having a load of your things arriving when you’re only there on a VV.  Maybe the first 2 options would be safer - store in the UK then ship it out when you have your visa in place.  Once you get jobs it shouldn’t take very long at all to get WPs and you can start the wheels turning to have your stuff shipped out.  

I think it still applies that flying with Air NZ via the US you’re allowed extra baggage allowance of 23 kg. x 2 each.  Still not enough for what you say you want to bring and it’ll be a struggle shifting all those cases around, but it might enable you to take more with you that you think you’ll need immediately you get there.  When are you thinking of going?  I have it in my mind that it’s around the middle of the year?  If so, that’ll be winter time in NZ and you’ll be needing your winter clothes with you.

If you want to send a box of items over to someone in NZ, they will have to see it through the MAF inspection, do all the paperwork and, I imagine, will be expected to know all about the contents in case any questions are asked.  Could get a bit awkward, especially if there's the odd item that doesn't quite conform to their rules.  

Your best bet would be to talk to several freight forwarders to see what they come up with by way of suggestions and prices.  You won’t be committed to any of them, but it’d give you a good idea of what you’re up against.  I think I’d be having a dummy run now by seeing how much I could cram into all those suitcases and then stuffing the remainder into one or more cardboard boxes, just to see how it all fits in.  If you do it now it, at least, gives you a bit of time to think about how you’re going to deal with it rather than leaving it until later on. If you need to store in the UK while you're waiting for your visas, the shippers can do this and you just need to let them know when to send it out.