I don't think many US pilots at EK/EY/QR would look to leave if their respective airlines offered 'reverse roster' like this, i.e. starting/finishing your sequence in your chosen US destination.

My only concern doing this would be that a pilot would probably lose/not qualify for foreign-earned income tax exemption status. I know if I were to get a gig like this, the first person I'd talk to would be a tax attorney to clarify this stuff.

Having said this, I doubt that any of the Middle East carriers would do something like this. It would be a huge bureaucratic nightmare for them… but then again, any Middle East company worth its salt employs an army of Indian paper pushers who love nothing more than mountains of paper and stamps, so it wouldn't necessarily be insurmountable.