Hi Deadpool,
Out of interest how's the conversation from FAA to EASA going? I'm trying to go the other way but haven't had much success with the FAA.
I would say with your background you'd be fairly competitive, although carrier's like Virgin typically want 2500 jet time. BA is another option, but their recruitment is fairly blocked up at the moment with lots of guys 'swimming' in the hold pool.
The big difference that you'll find is UK airlines will typically go through recruitment phases. They'll open for a bit, and then close. Sometimes this can as quick as a few weeks and so it comes down to right place/right time. It will also depend upon weather you get an unrestricted ATPL, or weather the CAA 'Freeze' you for 500 hours.
Just my views and others may disagree. If you've got the Green Card why not apply to the US Majors?