Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
I have some bad news for you: AA's one-way awards do not permit any stopovers outside of North America. So you would need to book a whole series of one-way awards to get to visit SIN, SYD, and HKG on one trip. And that will get expensive.
Another option would be to book distance-based Explorer awards, which do permit en-route stopovers. But you probably do not have enough miles for four Explorer awards in F; maybe in J. Suggest you take a look at the thread on Explorer awards; it contains a wealth of information.
As an aside, try to avoid starting your trip in LON: the UK APD charges will add up to a small fortune.