Bill, Paul has pointed you in the right direction.
My own understanding/experience/observation: It IS a factor against you, unfortunately, as far as applying from overseas to Asian schools. However, in person it can sometimes be a different story. Also, if you are willing to just go to one of these countries, you can, with any luck get work -even a lot of work, privately. You just have to do the visa run yourself every now and again. Thailand would seem the easiest for this. I don't know about China.