Your itinerary fits the CircPac 26K ticket (about 23500 miles or thereabouts). It still may be cheaper than a J OW fare. If you can get the trip down to 22K miles, that fare is best value. You may be best starting the J trip in LAX (and getting a "cheap" fare DFW-LAX-DFW) so you can squeeze in BKK and PER.
You certainly can go SYD AKL LAX DFW YVR HKG SYD for the 22K - but BKK and PER just don't make the 22K cut-off.