Here's to a crazy idea, but since QF doesn't get on with CX, and now doesn't get on with MH either, perhaps QF should leave OW, and join ST. Virgin is somewhat aligned with *A, and with SQ obviously being in *A, that's not really an option.

But if QF does join ST, they would have instantly created a network in China, via MU in Shanghai, and to a lesser degree CZ which flies to major AU cities already. The link to Japan is lost, but with non-stop flights from eastern AU to the US, I don't see it as a big loss. However, they gain VN's network, and further collaboration in that area would also help with Jetstar's somewhat haphazard relationship in that country. And then, there's Garuda... but I can't see them being too happy about letting QF in.

QF also already codeshare with AF to France, and its frequent flyer program also earns points on AZ. But apart from this, the network does have a pretty big hole in Europe. Having said that though, given QF's recent strategic shift in focusing in Asia and regional flights rather than the ultra-long-haul segments to Europe, moving to ST actually sounds like a good strategic fit.

EDIT: Adding to the above, I've just been made aware that Jetstar Hong Kong is launching as a joint venture with MU. As silly and embarrassing it is for a OW founding member to defect, it does sound like it might just work out... (although I might not say the same after I recover from my red-eye flight).