The nearest job to yours on the skills lists that I can find is Bricklayer.
http://skillshortages.immigration.govt.nz/bricklayer/ Do you perhaps have the qualifications to do that work, although it isn't what you've chosen to specialize in? It is a skill that is in demand at the moment in NZ, because of rebuilding after the various earthquakes of recent years.
Notice, New Zealand have recently been tightening up on their requirements for visas. Anyone hoping to do what you are hoping for really needs qualifications. Yes, people in the past have managed to get a job offer while on a WHV and then get a work visa on the back of that, but it's getting harder to move on from work visa to residence.