From memory (and without looking at the rules), there must (should?) be a sector in the North Pacific. You don't have one. Also, I'm not sure you can use PPT since it involves QF codeshare on TN. Basically, I think you have to use LA SCL-AKL/SYD; QF SYD/MEL/AKL - LAX (or HNL then AA to LAX etc); and/or CX to HKG or AA to NRT. A routing such as SYD AKL LAX DFW YVR HKG SYD is legal (and under 22K miles).