I am looking at an award ex AKL to ORD in early 2020 and have been looking at options like you.

Looking at 330 days out AKL/HKG generally seems possible in J on a Thursday on CX but not other days of the week (based on looking at QF and BA). Unfortunately I couldn't see any availability HKG/AKL in any class on CX.

Therefore you might get AKL/HKG/USA on Thursday, 28 November or Thursday, 5 December when that opens up in the next couple of weeks. As you don't mention where in the USA you will be flying from I can't comment on the TPAC sector on CX, but that will probably be easier than the AKL/HKG sector

QF doesn't seem to regularly release seats at 330 days and in any case J is hard/impossible to find. I have however seen F seats ex LAX via SYD but it is going to be a matter of luck for 2 seats to open up on the day you want them. FJ is similarly random in J.

Good luck and I would be interested to know if you are able to get anything.