First off you are going to need a Green Card or at least an EAD (Work permit). No airline in the USA is going to sponsor you for one of these and the only way to get one realistically is to be married to a US citizen. Even then the process can still take upwards of two years. (I'm speaking from personal experience here).
After that you'll need to convert to an FAA licence. No matter what licence you have, if it isn't FAA, no Part 121 carrier is going to even look at you. As you have over 1,500 hours the easiest way to do this will be to get an FAA ATP. You will need to sit the ATP written (very easy, I passed after studying for a couple of days) followed by an ATP check ride and oral. The oral section is very comprehensive, so don't be fooled into thinking that you only need to study the question bank for the writtens and then you'll be fine. The oral section can be upwards of four hours long and is then immediately followed by the check ride. This can be done in a sim or in the actual aircraft. It's like a standard LPC. Once you've passed all of that you'll be issued a temporary airman certificate and you'll be mailed your permanent certificate within two months after that.
Getting a job in the US isn't too challenging at the moment if you have the time. You might get a look in at JetBlue, but realistically I would imagine that you'll more than likely have to look to the regional airlines for your first job. The majors over here generally ask for at least 1,000 hours turbine PIC in addition to at least 3,500 hours total time. However, nearly every regional is hiring right now, some in huge numbers. Your best bet would be American Eagle or Pinnacle, maybe even Republic. I applied to a number of airlines and with every application, bar one, got invited to interview within a week of applying. My total times are about half what yours are, but having a lot of turbine time really helps.
You'll be fine, as long as you can get the work permit issue resolved.
Good luck, and if you need any further advice, feel free to PM me.