LAVDUMPER,
I had about 4500 hrs on jet turbine aircraft when I applied and I waited about 18 months for my imterview but from what I hear some guys are getting interview dates as quickly as one month from applying. It seems that EK are looking at jet turbine (at least 1000 hrs) rated guys. Also they seem to be looking at multi-crew ops and an airline background (though not mandatory). I am currently on the Airbus fleet but it seems that there are no choices of A330 or B777 for new joiners. I think EK puts you on either aircraft type based on the availability of transition courses and new aircraft arriving.
Good luck.