I can get work short term via the LAT scheme
Are you sure about that?
The Council will not grant an authority to any person who is already eligible for registration; they would need to go through the normal registration process.
http://www.teacherscouncil.govt.nz/prof/lat.stm
And
19. A person is NOT eligible to apply for a LAT if any of the following apply:
• s/he is to fulfil a role not defined as a teaching position
• the position is sole charge
• s/he is a registered teacher or has approved teaching qualifications
• s/he holds a practising certificate or is eligible to hold one
• registration is not compulsory for that position.
p. 63 here
http://www.teacherscouncil.govt.nz/r...olicy_2012.pdf
I'm not saying this to be wanting to be a wet blanket, but from what you've said, you may be burning some boats already in setting out for NZ, and I'm sure you don't want to find more hurdles in your way than you're prepared for.