OneWorld Explorer in economy is booked in L fare bucket. AA do not give any points or SC's to QF FF members for fares booked in L. So you want to use any many QF or CX codeshares in the US as you can.

The HKG connection between AKL-HKG-LAX must be transit only - ie less than 24 hours. Note that on the CX leg HKG-LAX you won't earn any status bonus points, so depending on your status, you may actually earn more points by using QF trans-Pacific (but less SC's).

In Europe, ovoid BA if you can. They only offer QF FF's 25% base points on L fares. But again, depending on your FF status you may score some bonus points as well. Look for AY or IB flights to get better points. Look to use AY or IB for the Trans-Atlantic service if you can. unfortunately I can't find any AY (or Ay codeshares) that are over 5000 miles. AY do codeshare with AA for some trans-Atlantic services (eg ORD-CDG). You can get more SC's using BA on SFO-LHR, but less miles due to thr 25% for L fares on BA.

Coming back into Australia, try to take CX from HKG-NRT and the QF NRT-MEL for a good points/SC earner. And MEL-PER is not considered Australian Trans-Continent, so you can then return PER-SYD.

Of course, most of these comments and suggestions are only relevant to the L fare. Its a very different story in D or A. But those fares are a very different stort too .