Thanks!
By the time you mailed your answer I was on my way from Pretoria to Dar-es-Salaam, carrying US$ 6600.- in cash on me. It is not something I would advise anybody else to do, but I am glad I did and nothing bad happened to me. As you say, South Africa has a good banking system, and I took out the necessary amount of ZAR in Pretoria to buy the 6000.- $ (the 600.- $ I already had) on my MasterCard. But regarding how often I was absolutely the only tourist, like on the Livingstone-Kapiri Mposhi and Dar es Salaam-Mwanza trains and the Zanzibar-Mombasa "dhow" I am glad I had cash and did not have to rely on being able to use travellers cheques or card.