As far as I know you must send a valid passport. You can get a temporary passport from DC embassy or Nepal consulate in New york.. I think it takes around 7 days to get your temporary passport. While sending a temp passport write a letter stating why you are sending temporary passport. when you apply for temp passport, apply for MRP as well. One more thing if you personally visit Consulate in newyork they will return your passport on the same day. You will need
1) application forms - you can get it there
2) Passport photos - I think you need 3 of them
3) your original passport
4) your original citizenship.

if you have any question, please call them.

Nepal Embassy - Washingto Dc
(202) 667-4550

Consulate General of Nepal - New york
(212) 370-3989

good luck.