With Oneworld I also could do LAX-LIH-(surface)HNL-SYD, then I would only have to use one local flight LIH-HNL (who needs more short flights on such an itinerary). But the problem is that in the booking tool I can"t find any availability for direct flights in the period I need them (around Oct 15th). I can only find flights through LAX (not allowed) and NRT... So this won't work.
In combination with the rather complicated route within the US (no direct SFO-LAX) so I gues Oneworld won't particularly work for me...