Employment in the US has a lot to do with connections, If you lack PIC and you are a resident vs. a national, it is more difficult but not unheard off to obtain employment with one of the carriers here but applying from abroad is going to be an uphill battle.
I don't know why you want to make such a move, living in the US is not cheap except in areas where NO major carrier has a base and then you will become a commuter. Let's talk about that for a second, If you think the London traffic is hard to deal with, wait until you face the friendly gate agents and some mainline crews in your commute to and from work, all of the sudden the traffic in Puerto Prince is not going to seem that bad.
Here are some options, I think that the best way to get some PIC and relationships for references would be to target a regional carrier that their pilots are leaving for the major that you want. Any which way you choose will be a hard and long process because you will join thousands that are trying to do the same as you and that have the pic and references to work at it.
One warning about Flightinfo, Too many children and frustrated bitter individuals posting their views as fact. Not by any means and stretch of the imagination a reliable source. Is more a source of entertainment than information. More like watching an episode of COPS raiding a trailer park. It makes you want to throw up, but you still want to see how is going to end.
Good luck with your decision. I'm the opposite of you, working here with tons of references with different carriers and plenty PIC but looking for employment abroad. Go figure
