Yep, as serfty said, one has to go AKL to LAX direct to get the ticket issued by AA, or the online tool will reject your itinerary.
For reference, I did very similiar routings for the following and here are their prices (all converted to NZD).
First leg is AKL-LAX with AA number = $13499.00
First leg is AKL-SYD, then to LAX, all with QF numbers = $14038.10
ex-JNB, QF number = $11434.76
There are even award seats to reposition myself to JNB too...!
I wonder if they will price me ex-AU if I try to pay online with an AU card (if I go with an ex-JNB ticket)...