You could also use a travel agent to book. There are some pretty experienced agents around. You pay a fee, but booking, changing flights or even the routing is much, much easier that way.
I book everything else myself, buy I find for RTWs the money for the agent is well spent.
Also keep in mind that you can do 16 sectors. You could add a trip to the middle east at the end (as long as you don't touch your starting point. And I think you cannot have more than 2 stopovers in your continent of origin and also no two stopovers at the same city.
Or you could add another place from HKG (Japan, Bali?)
If you run out of sectors: You could go LHR-BKK on BA if you don't want to stop in HKG, then go to HKG later and to CNS on CX, then do SYD later. Just some ideas.

Personally I would do the trip in Business Class, but then the additional cost is significant. For me it s much easier to get over jetlag when I can lay down and sleep, you also can use the lounges, priority check in and have a higher baggage allowance. But then you never want to go back to economy on long flights.