(1) I am sure the other airports in the area might allow  temporary passage;) Worth a shot. Check the nearest grandparents airport, if applicable - grandkids in distress melt the hearts of even the most heartless air-traffic controllers at such airports :) Grand uncles and aunts, if applicable, might be able to provide temporary passage too.

(2) The other option might be to frame this to your parents as a temporary and exploratory visit  to figure out if you can live in Nepal. Presenting them with  a rough time-frame (3-4 months) might make them more amenable.

(3) Or if you want to get really Machiavellian,  you could say you are visiting to research a thesis (or theory or whatever) and need a place to stay while you do your work. The idea that you will be productive while you are there might make them to look at things more favorably  - I speak from personal experience on that one. :)

Good luck!