AA has flights from SYD to LAX and DFW, but IIRC they're all QF operated codeshares.

Virgin serves Brisbane and Melbourne currently (as well as SYD), although one of these is supposedly switching to DL flights as part of their JV.

UA has flights to SFO as well as LAX. IIRC their MEL flight stops in SYD.

Under some conditions, mideast carriers provide a hotel room for overnight connections. On some business and FC tickets, they provide limo service to/from airports. You might also be able to get a stopover in the mideast or Europe (or possibly even SIN/BKK) for free.