Soupy,
As gspinz says, if Air NZ only has a few maintenance traininee/apprentice places, maybe you would be better off going elsewhere.
Try looking at all the other aviation opportunities around you, such as the expansive NZ helicopter fleet, or bizjet fleet. There must be other Commuter Airlines around the Islands?
I know your likings may be more toward the big stuff, but try starting on the smaller stuff.
Although these aircraft may be smaller, the mechanical theories are all very much the same, and many of the avionics are very similar in the bizjet/commuter fleet.
You could get to know much more of how the whole aircraft worka (and 'all' of an aircraft - as opposed to 'parts' of a larger aircraft) This is all "experience" - and you may even like it enough to stay there!
I started on Helicopters, went through Flying clubs and fixed-wing maintenance to get to 767's - It can be done!
Oh, and Nothing in aviation is easy!