As for places to visit why not ditch SIN and add GIG albeit it would mean you'd hit SYD sooner and I'm guessing you want to spend Xmas in SYD? If that's the case I'd still ditch SYD and spend more time in HKG (day trip to BKK?), SYD and NYC.

Have any of the travelling party been to these places before? If so I'd probably be tempted to ditch them in favour of new destinations.