I can't find any rule that prohibits your surface sector and flight between Australia and NZ.

Since you also have several flights within Australia, double check that you don't have more than 1 flight that goes between either Perth and BNE/CNS/SYD or Darwin and MEL/SYD.

The only way you could do SYD-HKG-LAX is if you had come to Australia from Europe on a single plane service (no stopovers or flights within Asia on the way to Australia other than a few hour plane refuel in SIN/BKK). If this is how you came to Australia, you could do several Asian stops after Australia before continuing to LAX. Stopping in HKG adds a great deal of time to your flight to LAX (9 hours?), but hey it's Cathay so I understand the idea.