As depressing as this sounds I'd say staying at your regional and pursuing PIC time is a better choice if you really want a US major airline career in the long run.
You just don't get the maturing experience needed to compete for major airline job being SIC in any sort of operation. Another part of it - that overseas carrier is not operating by FAA standards and is not under FAA supervision. It is a big red flag.
Also, besides the flight hours I suggest you strengthen other important aspects of your application. You have to have leadership, customer service and preferably volunteer experience. Remember - recruiters are HR folks, not pilots. Make sure you get involved in your community, housing association (talking about it was 80% of my interview), maybe some volunteer organization, always go out of your way to help passengers - a couple of thank you letters from your CP will go a long way too.
Good luck!