Ok,
I found that Travelocity.co.uk has some good fares. As low as 632 UK Pounds (under EUR900), taxes included, if you change to Dusseldorf-Cape Town from Dec. 23 to Jan. 9 (1st screenie). A matrix with different dates shows the fares possible (2nd screenie).
I'm guessing you should be able to book as a European on travelocity.co.uk.