Actually it great degree but just not for immigrants fighting for status/job/stable income . Most people who take these degree are from prominent family at lest higher middle class , who will eventually do some other joint degree like law or business management . Lot of them end of being some local or federal politician .

May be you should consider taking additional law degree or some joint degree in economics . But immigration is other story, not sure how easy is it for lawyer to get h1b and gc. Job wise eventually you will get some teaching position in liberal arts college any way, and if you take law degree you can have some law practice. For immigration may be you should choose some other way out , may be get married if you are not yet.

IT may be temp fix , but it might get painful over long run , considering jump u are making .