@JRSK:
You should be offered an interview within the next two weeks. I submitted my application and two weeks later they offered me an interview in DXB.
Some people love and others dislike EK. I think you need to decide if you can stand missing the hiring wave in the US. If you go to EK now you'll miss out on US Airline seniority.
I would think that pay and QOL at EK will have to improve as the pilot shortage sets in. I may be wrong, but pilots will become an even more valuable commodity in the middle east.