Go to the next FRRO and check if they are willing to endorse your visa for two weeks. I've been to the FRRO a few times on other matters and the waiting room was always full of tourists requesting and extension or an exit permit.

http://boi.gov.in/content/general-in...ion-foreigners

It is not impossible. Do not use an agent, many FRROs had a few corruption scandals and an agent may not help you.

If they are too picky/blocking, fly to CMB/KTM/DAC etc.

Do not overstay!