I am pretty sure you would need a visa as you have to literaaly enter brazil as you have to go to the SAA ticket counter to check in if using a ZED. Something similar hapened to me in Chile, were you dont need a Visa but you need to pay a pesky entry fee ($140 back in 09). I flew in on LAN from EZE to SCL and was just tranfering on to AA and needed to check in at the ticket counter. They made me "enter the country: pay the entry fee eventhough I was not technically leaving the airport . This is all red tape bureacracy which is pretty common in Latin America "I know since I originate from this part of the world". Anyways I am pretty sure Brazil requires the Visa even if you are just transisiting. However, I would say your best bet is to contact the Brasilain Embassy via telephone.
keep in mind SAA also flies to EZE (from JNB, no Visa needed for Americans traveling into Argentina but you need to pay an expensive entry fee for each pax in the party.
Other options worth pondering can be HKG -JNB (which both saa and CX operate).

Regards,

Chepos