I can't say I'm surprised by AA's decision given you have no AA flights on the trip - do they codeshare on the JNB-LHR flight and is it possible to book the codeshare stand-alone without flying AA trans-Atlantic?

In the distant past (the last time ex-SA RTWs were cheap) I booked several 1st Class Oneworld Explorers through Flight Centre in Cape Town. For the 1st ticket they required a photocopy of my credit card. Given they have multiple branches in London you might be able to organise some way of providing proof of identity through one of the local offices and pick up your ticket in SA. I'm sure the possibilities will depend on whether travel agents in SA still get paid a decent commision or not. When i was buying my tickets it was around 7%. So they were making $400 on the deal and were willing to go a bit out of their way to accomodate me. These days I don't know.