Well if you can get over the immigration problem, then the next hurdle is the 14 JAA ATPL exams(can be busted out in 6 months if you're pushing it hard). I'm just finishing up mine now, and I can tell you, they're nothing like the FAA tests. They're laden with lots of irrelevent information, as well as relevent information that is way too in depth, that some lunatic deemed necessary to fly helicopters. The the big one is the JAA instrument rating which will set you back, now you're gonna need the Vaseline for this one, about GBP£25K-GBP£30K.. You'll more than likely need that to have a good hope of getting work over there. Although with 3500 hours you might find something without it.
Your best bet might be Vegas or the GOM(especially with S76 time). Although I have heard a rumor about lay-offs in Vegas last night through a friend of a friend, whether it's true or untrue is another story.
Sorry for the pessimistic outlook, I'm normally quite an upbeat guy!!!
Just out of local curiosity, where are you working now?