If you don't mind KE (searchable on the AS website), there is decent J availability on LAX-ICN-SYD RTs. You can even find all four segments on the A380. Only caveat is you have to book the RT, or be willing to book OW at RT cost.

There's also been some QF J availability YVR-SYD. I haven't checked SFO-SYD lately, but that is another option. The 744 flights might be a little easier to find than the A380 flights.

And don't forget CX through HKG, searchable through BA.

Be willing to consider BNE, MEL, ADL, and PER. With your wide range of dates, you should be able to find something at the 330 window.

I've managed to book QF F once or twice a year for the last five years, so it can be done.