You may have already gone and returned but I work in RSA and live in Denver, I always take this route...
DEN-FRA-JNB-SIN-NRT-LAX-DEN
I love SQ so this routing give me 3 SQ segments, the Spacebed in business class really is comfortable and nearly flat. I have also done DEN-FRA-JNB-SIN-SYD-SFO-DEN but don't recommend it. Flying back below the equator from SIN-SYD makes little sense to me unless you have biz in OZ.
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Kevin