Do Qantas still code-share with Gulf Air on Singapore-Bahrain-Athens, if they do this could be quite a reasonable possibility

Qantas are quite stingy on award inventory. Recently on a trip to Bangkok Qantas wasnt willing to give any Y, J or F Class tickets on QF 2 or QF 302 but I was able to book under a BA flight number (in First Class mind you).

It's all a matter of luck I guess