This may work better if you don't mind going the opposite direction.

LAX-PPT-LAX-SYD-ICN-SIN-ICN-BOM-NBO-JNB-CDG-EZE-ATL-LAX...you can throw in some 23hour55m layovers in there somewhere since that's only 13 segments or replace an existing stop with one that requires more flights. Also note that AF has a nonstop EZE-CDG flight.

Also jjglaze77, the MH flight is EZE-CPT-JNB-KUL...twice a week...22 hours total for one whole flight! Its a shame we can't include MH on RTW awards.