I believe that you are making two mistakes.

1. Going east rather than west means an overnighter on the transatlantic leg and possibly other flights rather than a day flight where you can maximise the experience.

2. You are missing a transpacific sector in CX F.

I would do this itinerary instead.

LHR-SFO in BA F
I have been to LA. It is a hole. Don't bother and go to SFO instead. LHR-SFO is a nice long day flight departing at a civilized hour.

SFO-Hawaii-SFO in AA F
Side trip to Hawaii and back to SFO

SFO-HKG in CX F
HKG is an amazing city. And CX F is meant to be amazing too. This dayflight is on my wishlist.

HKG-LHR in CX F
To take the dayflight.

If there is a JL F dayflight from NRT to LHR it might be worth heading up to NRT and taking it to experience this product instead of HKG-LHR in CX F, which you will have experienced on the trans-Pacific.