ExXB,
There are actually 9 business class fare possibilities on EK for the ATH-JNB route, ranging from 1043EUR to 6450EUR. Note that this does not take into account any historical sales fares that the OP might have bought his ticket on.
The two currently showing in the 2k range are 2054 and 2604 (CEEESGR1 and JEEEFGR1)
Reading through the rules now...
Hmm... well I'm no expert but seems to be those fare rules certainly look quite generous, so I'm guessing when you hit the 2k+ mark on EK, you are in semi or fully-flex territory.
So, to the OP, I guess its a case of as ExXB says... get on the dog & bone to EK and see what you get.