Since you're booking in J and have segments to spare (I count 13 including your OGG-HNL surface sector), I suggest a few tweaks:

Are you flying JFK-LAX-OGG in order to get a 767 JFK-LAX? Because one consequence is that LAX-OGG is on a 757. If you fly DFW-OGG, you'll get a 767. Much nicer plane for the long flight. You could go JFK-LAX-DFW-OGG, or LGA/EWY-DFW if you want to avoid adding an extra sector (but you have three spare).

LHR-JFK is a rather short flight. I'd suggest LHR-LAX instead. You can go LHR-LAX-JFK if you aren't flying JFK-LAX to start (only one transcon).

You asked about LHR-JFK. If you'll be in J and on AA's new 77W, I'd go with AA for the new J seats. If you do decide to fly on BA metal, ask for it to be an AA codeshare to save a few hundred dollars in fuel fines. However, keep in mind that you can upgrade AA and BA flights using AA miles or BA Avios. If this is at all possible for you, it'll be a much nicer flight and make it all the more reason to fly LHR-LAX. I'd take LHR-LAX in F on a current AA 777 over LHR-JFK in the new 77W.

So, my suggested itinerary:

AA: EWR/LGA-DFW-OGG
QF: HNL-SYD
LAN: SYD-AUK
AUK-SYD (LAN) - SYD-CNS (QF)
QF: CNS-BNE-SIN
CX: SIN-HKG
CX: HKG-DBX
BA: DBX-LHR
AA: LHR-LAX-JFK

You'll still have two sectors to spare if you wanted to add another side trip. Perhaps LHR-BCN-LHR? Or if you want to earn more miles, LHR-TLV-LHR.