You still have 2 trasncons (lax-sju and lax-jfk) so you can't do lax-jfk-syd, but will have to just do lax-syd (or go eze-jfk-syd and not eze-lax ... btw you are right there is an LA flight EZE-SCL-LAX that is a single flight number, but it is sold as F only SCL-LAX and not EZE-LAX).
ZRH-JNB-LHR-NBO is prohibited (you can't enter Africa twice, see the earlier explanation by christep). So you have to fly JNB-NBO (operated by Comair/BA in South Africa).
The biggest problem is that I think you cannot transit Europe twice, so you will have to go HKG-JNB-NBO-LHR-(europe segments)-LAX. I'm 95% sure that this is the rule (basically a 2nd entry into a continent is allowed only when no realistic alternative routing exists, and sometimes the sequence of continents is forced by the rules).