Check Airman I think that one of the first hurdles you need to overcome is your way of thinking.
There is NO SENIORITY in a contract job. There is no bidding. You are hired help that gets assigned the tasks or trips that locals don't want.
Some of the Japanese carriers are unique in that they will upgrade F/O's, but that is VERY rare. Consider also that when JAL hit a rough patch 3 years ago, ALL their contract pilots were given 30 days notice; you are expendable. There is also no such thing as a recall, just "sayonara" gaijin.
In the current economic climate you need to consider the risks of leaving your current employer, no matter how dull or dead-end the job may seem.
Another risk not previously mentioned is that you will probably be operating well outside the protection of the US (or any other reputable country) legal system. An agency may indeed be based in country A, but their "related entity" which actually sends you the contract may be based (nominally) in a country that you have never heard of, and which just happens to have a very "flexible" legal system. Many pilots have been caught out this way; get screwed over by the agency, and have no recourse through the courts.
Contracting can provide an interesting and varied career, but times are changing, and there are just too many bottom-dwellers out there.
Carefully consider all your options.