.... starting with MEL-NRT.

You need to get the RTW ticket to do the 'heavy lifting' - long-haul flights, so you get maximum bang for the buck for your 16 segments. You have a lot of short-haul European segments (ber-ams-cph-cdg-mad-zrh-vie-mil-bru -- 8 segments for just over 4,000 miles) - I would do most of those as a separate ticket(s) or by train (probably just as quick in some instances and perhaps much more interesting). Likewise, I would do SYD-MEL as a separate ticket and go SYD-MEL-SYD, as you'll need to go back to SYD anyway to get directly to NRT.

Likewise, New York to Toronto and then Mexico City - I'd look at New York to Toronto and back to New York and then start the RTW ticket.

You also can't do direct JFK-MEX, MEX-GRU, PEK-TPE, TPE-JNB.

Do you have to go in the specific order you've identified or is there some room to change the sequence of cities? Is New York a required city? You can start a xONEx in Canada (Toronto) and end in the US, so that's not a problem. Also, a LONE6 ex-Canada is slightly cheaper at C$6,000 or currently about $5,400+.

Edited to add: Perhaps something like -
yyz-dfw-mex-eze-gru-eze-syd-nrt-pek-hkg-tpe-hkg-jnb-lhr-ath-lhr-dfw
16 segments, 44,726 miles.