Hi and welcome.
Firstly I would mention that INZ does not look kindly on overstayers and people who are or have been illegally in NZ, so I would find out first if they would entertain any further visa application from you before you go to the trouble of getting everything ready.
If you read
Kiaora's story you will see that she had quite a struggle with them although her overstaying was in Australia and not NZ. However INZ was very concerned that she would overstay again if they granted her another visa. In her case she and her fiance wanted to settle in NZ and have children there, but you appear to only want a temporary visa so I don't know how they would look on the fact that you don't want to put down permanent roots there.
In my opinion, I think contacting INZ directly to ask the question if you could make another application would be the best thing to start off with. They will have it on record that you were illegally in NZ.