Is there any way to avoid Europe and North America if you're doing a DONE4 with a route Africa-South America-Australia-Asia-Africa? I couldn't find any flights from South America to Africa...

I hope to visit South Africa, Namibia, Peru, Chile, Ushuaia (Argentina), Easter Islands, New Zealand, Melbourne, Darwin, Bali, Singapore and Bangkok on a DONE4, but can't see to figure out a way to do it. Ticket would be quite cheap in MRU, so that could be an ideal starting place, but other suggestions are welcome. I'd like to fly westwards and am based in Europe, so including Europe could be an option after all...