your question is confusing..
Should you file for TPS ? --- You should know that better than any of us.
Do you qualify for it ? -- If you were here during the quake and the initial registration period 6/24/2015 -- yes you will qualify for it.
It takes around 3 months for the TPS according to USCIS. but generally 2 to 2.5 months.
My suggestion:
File for TPS and file AP(advance parole travel document) , leave the country after the bio-metrics appointment so you don't overstay on your L1. AP will let you come back to USA.
Not sure if L1 has a grace period after expiration but if it does I would file the TPS asap.
If you can go back to Nepal and comeback with your current L1 , then you should be fine as well. Make sure you don't miss the bio-metrics appointment though.
