Thanks! I played around with the online tool today, and business does indeed seem to have better availability.

If we were to book business, we'd probably fly from Stockholm. My buddy works there, I have family there, and the latest spreadsheet I saw seemed to indicate reasonable prices from there. So 16 segments:

ARN-LHR-EBB//JNB-WDH//VFA-JNB-CPT-JNB-SYD-CNS-SYD-SCL//EZE-LIM-MAD-ARN

Gardyloo, I like the Easter Island suggestion, I'll see how that fits into our timing. I'd looked at it earlier, and the flight timing meant staying there for 4 days, which seems long, but maybe there's more flexibility in business.

-Nick