Doesn't matter how you get from ADL to SYD or MEL, you'll have no check-through and no interline. You'll have to pick up your bags, go to the international terminals and check-in for your international flight.
If you are taking the SYD-BKK TG flight in the morning (the one that most likely has the availability and the one that is most able to link up with SQ flights BKK-SIN), the first flight of the day ADL-SYD is barely going to get you there on time to make the TG flight. You'd have about 30 minutes to get off the domestic service, get your bags, high tail it to T1 and then check-in before the cut off. Then you'll not have too much time to get so much as a drink in the lounge before you board. You could overnight in SYD instead.
As MEL_Traveler said, if you can get a TG connector for BKK-SIN, at least you'll have TG F lounge access in BKK for all your troubles and extra cost, which will include a full body massage if you allow at least 60 minutes connecting time.
On the balance of all considered, especially if your other half does not enjoy transfers, I'd probably go for the direct via MEL. SQ may run one A333 service MEL/SIN daily which doesn't have fully flat J seats (same as the older J seat on VA's coast to coast A332 services), but if this doesn't phase you or if your predicted equipment is a B777-300, then that's OK.