From a wargaming possibility and visual spectacle point of view I very much like your idea but the Perry Koreans are late 16th C. from the time of the Japanese invasions and the Mongols as such had surrendered to the Ming, who eventually came to the Koreans aid against the Japanese, over two hundred years earlier.
My Mongols are mainly Curteys which I know are very marmite but you could look at all the various nomadic tribe ranges like Khitan, Hsiung etc. along with Huns from the likes of Gripping Beast, Essex, Bears Den and even Old Glory to make up a very interesting and diverse force.