A bit more tweaking and it looks like I can go this way:
BNE-SYD-LAX-DFW-PHL-ORD-NRT-BNE
This gets me skybeds SYD-LAX on QF107, and AA 763 LAX-DFW. Just have to put up with NRT for about 5 hours connecting to a QF763 for the return journey. This is 21,866 according to Great Circle Mapper. And will earn 600 QF SC's.