My guess is that you will never see basings for the simple reason EK will never accept their crews being subject to OZ/euro/North American labour laws.
If anything we may see some attempt to introduce commutable rosters. Against this is that it would require more pilots because there will be less guys available in DXB to work days off to cover shortfalls. This is also contrary to current EK policy.
Will the market become tight enough for EK to change their position on these issues?
I think we are still a fair way off that yet, judging by the guys who are still coming. We haven't even started tapping the turbo prop market yet. History shows that EK is not forward looking in these issues. They tend to roll the dice and gamble that somewhere another airline will go broke just in time to provide the required amount of pilots. Remember we are not looking at huge numbers, only 250 a year. Given that EK can source from anywhere in the world (unlike Virgin, Qanas or J*) I would say the odds are in their favour, and so far history would support that.
V