The "fly westbound" thing has a sound physiological basis, but Oz is so far away that it doesn't work.

The reason is that our body clocks would, if left to their own devices without the input of sunrise and sunset, run on a cycle of about 25 hours. So if you fly somewhere that's distinctly to the west, your body will find it quite easy to catch up as it can do it while following what it would do anyway but for this pesky Sun that comes up too early every morning. (And don't we all know what that feels like.) If you fly 5 time zones west (London -> New York, for example), your body clock resets itself much faster and much more naturally than if you fly 5 time zones east (New York -> London), when it will really battle to get back in synch with the real world.

But if you fly somewhere that's 11 time zones away, as Sydney is at this time of the year, it frankly makes no difference which way you go. Your body clock is going to be battling in exactly the same way. And it's so many time zones away that a day or two in LA on the way isn't going to make it any easier than a day or two in Singapore.