How about this:

CAI-MAD (IB)
MAD-LHR (BA)
LHR-DXB (BA)
DXB-LHR (BA)
LHR-HKG (BA)
HKG-SIN (CX)
SIN-HKG (CX)
HKG-MEL (CX)
MEL-DRW (QF)
DRW-BNE (QF)
BNE-MEL (QF)
MEL-SYD (QF)
SYD-JFK (QF)
JFK-LAX (AA)
LAX-DFW (AA)
DFW-ANC (AA)
ANC-DFW (AA)
DFW-BZE (AA) - good diving
BZE-MIA (AA)
MIA-LHR (AA)