You can't go back and forth between Asia/SWP and Africa. Africa is in Region 2 along with Europe. Asia and SWP are Region 3. Only one transit between them is allowed. Also, you cannot use a SAA codeshare on a OWE ticket as SAA is not a OW carrier. However, there is a QF metal flight that flies JNB-PER-SYD.

Here is something that should work:

LHR-JNB-CPT-JNB-PER (or SYD) - HKG-DEL-HKG-LAX-LHR


This would be a 5 continent OWE ticket. If you don't need to stop in OZ, you can save some money and drop a continent by taking CX JNB-HKG.