I am pleased to report that the indentification of the mystery spider has been solved; here is the reply I received from the Queensland Museum:

That is a male Garden orb-weaver, Eriophora transmarina. This is a common spider and you are likely to be familiar with the female which is just a little larger (especially in the abdomen) and makes very large orb webs mostly at night. She lacks the special patch of spines on the 2^nd leg that he has. The males have this strange habit of suspending themselves by a single strand of silk from eaves and other vantage points with their front legs outstretched. I imagine they are smelling for females (but that is just speculation).

Another place to look for males of this species is as the dead husks left by the females in their webs!

The female looks so different that it isn't surprising we couldn't identify it as the books only tend to show the female; as you will see from this photo, it looks nothing like the one we have.