Its going to take at least 4 months. It'll eventually take longer once people start applying as the deadline day day gets closer, seriously backlogging an already backlogged application process.

There's also an option of traveling to Nepal on a travel document. Its a letter issued by the embassy that allows a traveler to travel abroad in the event that a Nepali national loses his/her pp or citizenship.

Also, its better to submit original nagarikta as this eliminates the citizenship verification process that causes longer delay. The embassy keeps your citizenship at the office instead of sennding it to Nepal.