Hi Corey,
to MoveToNZ.
Getting to stay long term in NZ is very difficult unless you can press the right buttons, which means having certain skills that NZ is desperately in need of and also the corresponding qualifications to go with them. Sometimes it's possible to get in with just a long and relevant work experience history or work experience undertaken in NZ.
The description you give of your work experience, it sounds like it's quite specialised and relevant to the areas you've lived in. Certainly carpentry is on the required skills list, but I'm not sure it would cover your type of work. Also, the fact that your previous employment has been casual would work against you as INZ would be asking for evidence of such employment and official records of this.
If you wish to study in NZ, you would need to be able to support yourself while you're there and you may find that the fees for international students are quite high. You can read up about Student Visas
here . It mentions about a type of visa where you can study part time while working for an employer if the two things are related, but I don't know if this would come under the term 'apprenticeship'. Have a look through
here to see if there's anything useful about apprenticeships in NZ. At least it may give you some contact details where you can get further information from. Sounds like you'd do well to contact one of the
co-odinators to ask for advice.
Certainly there should be no problem with you entering NZ on a WHV, which might give you the chance to explore your options 'on the ground'. Perhaps opportunities may arise that could assist you in your quest to remain in NZ.