With a little tweaking, you could probably squeeze into a Global Explorer which would allow you to use SA on that route. Specifically, if you do PER-AYQ-CNS-SYD without the backtrack to Sydney as you have it now then it comes to 33000 miles and you could route GIB-LHR-JNB-DUR-JNB-PER-AYQ-CNS-SYD-HKG-NYC-LHR-GIB.