Thanks for your very valuable suggestions.

So far I have made some tentative changes to my agenda. It now looks like:

cph-xlhr-cai-lhr-bkk-kix-hnl-xlax-xdfw-sjo-xmia-sju-jfk-gig-xlhr-cph

cai, bkk, kix, hnl, gig - are musts. (KIX= Osaka, I had to look it up)

It is difficult to optimise Miles vs. the place I want to go.
Still open to suggestions for improvements.