I found out the taxes:
The base fare was actually calculated as ZAR40020 and taxes are ZAR3542 plus ZAR233 for a total of ZAR43795. This equals just a smidgen under AU$6000 which is very nice indeed!
So by avoiding LHR and going through AA, taxes were only 9% of the base fare.
I scanned and emailed my authorisation and identification instead of faxing and it was fine.