Some Ideas:
Instead of LHR-CPT-JNB-HKG you could do LHR-HKG and in addition DFW-EZE-DFW or JFK-EZE-JFK.
Would result in 2500 additional miles, same amount of continents (no stop at one US entry, so you need to change segments around). Same number of continents, but you have tu suffer AA F vs. BA/CX F.

Also keep in mind that some of the US flights are on single aisle flights on AA - F is torture on long (esp. night) flights.