I just spoke to SAA reservations in FRA and they told me that SAA sent out "several" empty aircraft to FRA yesterday to try to get the people stuck in FRA/LHR/ZHR to SA tonight. They were not able to tell me anything about flights scheduled later than today and asked me to call again every day until.
The person did say that they would be trying to keep sending empty planes here and it didn't sound like they were diverting people to other airlines (yet).