If you are stuck with two stopovers in London, you can substitute Manchester (e.g. fly US-MAN) as a way to eliminate one LHR stop. Excellent air/train service from MAN to London if you need to get to London, otherwise decent MAN to Europe connnections. Plus Manchester is a surprisingly nice city in its own right and the airport is very efficient. Your other option is to fly CX to HKG from one of their other gateways (FRA, FCO, CDG, ZRH).