Originally Posted by ajnaro

I changed the order of your stops, but the following appears completely legal

JNB-SYD-Nou-SYD-AKL-SYD-hnl-DFW-atl-lax-LHR-ATH-MAD-LHR-JNB

You still have two segments left over for creativity. If you want to break the journey at the end of the visit to the US you will have to fly to Melbourne from LAX. You could add a round trip from lax to any city in the continental US (no east coast) and leave from there. Or, depending on the time of year, you could add lax-anc-lax.