Expediting the process isn't worth it unless you're willing to pay $300 as opposed to $150 for normal processing. You might wanna call the embassy's passport section to be on the safe side. 

In worst case scenario, you can get a travel document issued by the Nepalese embassy that's valid for 3 months. Paying $40 for it will make far more economic sense than applying for a new passport. 

Enjoy your Khasi/Chyangra/ranga.