There really aren't any Asian majors that "like" U.S. guys over anybody else, but there are some that have hired a few of us yanks. Like posted above, Cathay have a few Americans, (Tons of Canadians though). EVA has lots of Americans, China Airlines, Emirates has a few, (Tons of Canucks there also). You can also try Sri Lankan, I believe they just recently hired some ex-United guys/gals, as they were Airbus typed. They have an all Airbus fleet. In Japan, Jalways ( a subsid of JAL) hires Americans, but only through crew leasing companys like those posted above. You can also try JALEX. Another JAL subsid. Qatar is hiring Americans, as is Gulf Air. Korean airlines also has quite a few US guys there as well. You can also try Asiana in Korea. In the past, they also hired expatriates.
Singapore hires DEC onto the 777 if you are high time with widebody experience. They also have a few Americans.
Hope this helps,
Good luck.