I was happy enough with my flights, and it was getting close enough to the date that I decided to book... and lo and behold, the online site couldn't process my credit card.
So I called up the local (Tokyo) Qantas office and for the first 10 minutes she gave me the roundabout saying there was nothing they could do for online ticket payment, if anything I'd have to go to the Joburg office in person (!!!), but with some prodding (it was a 40 minute call) she managed to a. give me a booking number, and b. send a message to her Joburg counterparts asking them to process my card manually. Mentioning it was a business class ticket for 3 seemed to help get her into action - by the end she was downright friendly. 90 minutes after the call I received a very satisfying automatic email with payment receipt and confirmation that the flights were booked. So it looks like I'll be traveling for a while!
Thanks again for all the help!
PS Himeno, that sounds like a very busy 4-6 weeks a year! Here I am worried that I'm trying to pack too many places in, and I've got a whole year