You will not get a multi leg, multi airline, multi county ticket at a reasonable price. Point to point will be far cheaper. Go and visit a living breathing real travel agent in a travel shop with your credit card.

In post 1 you stated Thailand USA. Is that now Sydney-NZ-USA??
Air NZ will be the only airline to offer Aust-NZ-USA, but expect to pay a big premium $$ for that privilege. AA, UA & HA fly NZ USA, so may be able to have a Aust NZ flight. But having that as the first flight may be hard/expensive. Go and visit a living breathing real travel agent in a travel shop with your credit card.

One way Aus NZ trans Tasman fares can be cheap. Do not see any advantages in trying to combine with a long haul.

You are trying to make this harder, and vastly more expensive, than it needs to be.
In this part of the world air fares are basically simple one ways, without the silly conditions so prevalent with USA fares.