I just tried doing it in the online tool again
The first try (see two posts up) was with an ex-Asia itinerary, to match what the OP was trying to do)
This second try was on an ex-Europe itinerary (LHR-xHKG-xSIN-SYD-oHKG-JFK-LHR). Still no go.
As an aside - I priced up the itinerary (without the xSIN transit so as to make it valid) using both CX as the first carrier and then using BA. BA was GBP370 more expensive than CX.