Who would you be flying HNL-OGG-HNL? I don't think AA does these routes and even if they codeshare with someone, I don't think the codeshares would be allowed on an AONE. You might have to buy a separate HNL-OGG-HNL ticket, but I might be wrong on this point.

If you did take these flights out of the AONE ticket though, it would give you the extra segments you would need to do SYD-PER-MEL-BNE-SYD in AU as well as a second stopover in Europe at the end of your trip (LHR-xxx-LHR) and still stay under the 20 segment limit. I'd guess that an HNL-OGG-HNL return can be bought fairly cheaply?

One more thought - rather than going ORD-HNL-OGG, why not do the ORD-OGG non-stop and then buy a o/w OGG-HNL to meet up with the HNL-SYD flight?

And lastly, its worthwhile considering that CX's HKG-JNB may not be three class for much longer since CX is planning to convert the 343s to two-class planes.