Maybe you need to set more realistic expectations and constraints. On the expectation side: free SYD-LHR earned from a single AONEx! You need to earn 150K for an AAdvantage award SYD-LHR. This requires flying 60K base miles (or twice around the world -- possible only with careful route construction on an AONE5 or 6). On the constraint side: you eliminate all of the good SC earning routes (they are in NA). syd-hnl-ord-orf-ord-lhr is 15K miles.
You can do lhr-dxb-lhr-hel-lhr-hkg-nrt-hkg-dps-hkg-mel-per-bne-akl-syd for an addition 35K miles, or 50K total (presuming Emerald status you would then have 125K earned miles, or enough for business class SYD-LHR). This is in the Aadvantage program. Using QF or BA would require considerably more miles, given your desire for the SYD-LHR redemption. Almost certainly AA would be the best plan in view of that constraint. You do realize that SYD-HNL does not offer F, and is one of the worst J services offered by QF, so your trip is off to a bad start. As for F on AA, it is reasonably good, better than most airlines, just not as good as QF, CX, or BA though I have sometimes picked AA over BA on some flights in F due to better scheduling -- it does offer a fully flat bed with state of the art seat and lots of space. Much nicer than J on QF for example.