For me the only 3 F products worth flying in your scenario are TG F, LH F, and NH F (OZ F is good but only worth it on A380/777 - and I don't think either is on a European route).

I would do the following:

CPH - FRA/MUC - BKK (LH J / F)
BKK - NRT (TG F)

This gives you access to both the FCT in Frankfurt (or LH F lounge at MUC if you can't get on FRA flight) and TG F ground services / spa / lounge in BKK (only get the full deal if you are departing BKK in F)

On the return I would do:

NRT/HND - FRA/LHR/MUC (NH F)
FRA/LHR/MUC - CPH (LH J / SK J)

This would allow you to sample all 3 F products and also benefit from the key lounge access opportunities.