You can also skip London altogether (now there's a good idea) and ride Iberia to JNB, switch to Comair to VFA, back to JNB and on to CPT, then CPT-JNB-MAD-JFK.

Ticket would read JFK-MAD-xJNB-VFA-xJNB-CPT-xJNB-MAD-JFK.

Tough to do on the "multi-city" options on aa.com because aa.com keeps defaulting to BA codeshares to JNB; but if you start in MAD you can bring it up easily. Might need phone booking ultimately, but certainly doable.

IB codeshares on Comair to/from CPT but not evidently to/from VFA.

Just a note - OT and political - the falls are also viewable from the Zambian side, removing the necessity of sending dollars to Mugabeland. In that case, the Comair flight into LVI - Livingstone, Zambia - is also quite acceptable.