tronek one other point which may be useful (my family are from/live in RAR so I'm familiar with limited flights to and from there), there is only 1 flight a week from LAX to RAR on Air NZ and your search confirms it is on a Saturday - I think you'll find if you look any other day the flight will ...

Hi tronekI'm not sure on the SC earn if you go via RAR however you can certainly fly firect from LAX to AKL on Air NZ without having to stop in RAR.