I just went through the process for a ticket US-SA. The only problem is limited availability to CPT, and no connecting options to CPT from JNB until *A.

I've gotten space on EK in Saver J to SA - just, as sbm12 says, use EK's own Skywards search engine to narrow the dates. EK will start a flight to Durban soon from DXB and I'm guessing there will be plenty of availability for this flight. Consider DL ATL-DXB nonstop if that's near you, connecting to EK to JNB/CPT/DUR. Easiest way of doing things.

Consider Kenya Airways as well from LHR or AMS for their 777.

VS has a flight to CPT but it is seasonal, unlike their flight to JNB; their lounge at LHR is great.

You may be able to get KLM at the lower rate in J; and they fly AMS-CPT and AMS-JNB.

I would recommend above all other options EK (for better food, booze etc).