You could do something like this: LHR-DEL-HKG-PEK-HKG-KUL/SIN-SYD-AKL-PPT-IPC-SCL-LIM-EZE-LHR on GLOBEX34 (39909 miles) and have the following additional tickets:
- SYD-MEL-SYD (with QF or DJ)
- AKL-WLG-AKL (QF, NZ and probably some others as well)
- AKL-NAN-AKL (with FJ/QF or NZ, you should be able to find it for USD 540 or even less(try a two segment "Visit South Pacific Pass", I did it on FJ/QF for USD 500 + tax))

Or a ONE4 with AKL-NAN-SYD on a two segment "Visit South Pacific Pass" with FJ/QF (the cost should be USD270 + USD270 + tax). For "Visit South Pacific Pass" look at http://www.solomonairlines.com.au/fares/vspcond02.htm