I downloaded the rules near the end of November 2016.
Rule 4(h) still has the limitation (referring to the 4 flights in the European area)
*not more than 2 of which may be between the UK and ALBANIA, ALGERIA, BULGARIA, CROATIA, CYPRUS, GREECE, MIDDLE EAST, MOROCCO, ROMANIA, RUSSIA west of the Urals, TUNISIA, TURKEY, UKRAINE.

It would seem for your selection, one of the two Middle Eastern points will need to be DOH and then connecting to somewhere other than the UK as QR does offer daily flights to most of the European area. The other choice might be:
HND-HKG-LHR-DXB-HEL-DXB-LHR-SFO.

Happy wandering

Fred