With a cursory look, I questioned whether your second LAX transit is permitted as I didn't think you could visit another continent again once you have left except on direct S Pacific Services. But in checking the rules, they clearly state:

Only one intercontinental departure and one intercontinental arrival permitted in each continent.
Exceptions: Two permitted in North America. when one is a transfer without stopover.
Two permitted in Asia when one is a transfer without stopover or on direct single plane service between the Southwest Pacific And Europe.

For a bit of variation, you might look at taking LAN or IB to MAD, and then up to LON. Of course you would then need to buy one extra sector within Europe, which would be permitted.

A further thought for flight timings, too, would be JFK-ORD-ANC (stop) - DFW-LAX, etc. Are you interested in accruing max mileage on this trip? Since you'll be on a 5-continent itinerary, you have additional segments you can take within Asia. You might want to nip from HKG up to TYO and then down to SYD with JL, for example. Otherwise, it looks okay to me.

Out of curiosity, what class are you flying and what fare can you get in Australia?