I am doing a similar itinerary just starting at JFK to London then Tokyo and Hong Kong to take CX F back to New York (As you suggest in your post CX F is fantastic. Also the HKG to JFK flight is 15 hours so is plenty of time to max out the experience). Unfortunately its going to be hard to go CX F on your itinerary without routing through HKG and CX don't fly to HNL.

You've had a couple of good suggestions about HNL and if you cant do the open jaw on your 241 and want to try CX F I would recommend

LHR - NRT on BA
NRT/HND - HKG on CX (JAL only offers J on this route) 30,000 plus £36
HKG - JFK on CX (105,000 plus £108)
JFK to LHR on BA (60,000 plus £252)

This itinerary will give you Concorde Room in both LHR and JFK along with the Wing lounge at HKG so you will be able to soak it up in best OneWorld lounges along the way.

Alternatives if you dont want to go via JFK you can go from HKG on CX and connect to BA for the LHR segment

HKG - YVR - LHR
HKG - ORD - LHR
HKG - LAX - LHR

Personally if you choose CX I would recommend going all the way to JFK, for the avios its really great value for the service plus you get Concorde room at JFK, Mrs P can enjoy the Spa and you will arrive into London to fully utilize the arrivals lounge for breakfast (which closes at 2PM). I would be really surprised if BA would allow LHR-NRT then JFK-LHR but then I would be surprised if they would do the itinerary you suggested too.

If your 241 is the only way to go, You might be able to get BA to do an Open Jaw LHR - NRT then HKG to LHR (leaving you to do NRT/HND to HKG as above). its not strictly RTW but its plenty of flying time and lets you max the 241.

Hope this helps

Chessy