Easiest award availability in J would be CX SFO/LAX-HKG-SYD/MEL//AKL-HKG-SFO/LAX redeemable on AAdvantage. Readily available if you avoid peak dates and have considerable flexibility. The non-stop USA-Oz flights are much harder to get despite more airlines on that route. A wildcard option would be DL/KE via Seoul using MR, also having good availability this year.