For all those people who are impatiently waiting for information regarding TWP. I was also one among you till yesterday. Here are some details that might help.
I applied for a TWP from US for myself, an open work permit for my spouse and 2 TRVs for my kids. I submitted the application online on Feb 9th. While submitting the application online, you do not need to sign any of the docs as at the end before submitting you just need to do a digital signature by typing your full name. The entire process is very straight forward and the best part is you do not need to send your passport until they ask for it.
I got the request for sending my family's passport (not mine) on April 26th and on May 2nd i got the intimation for sending my passport.
Even though the application was submitted online, my TWP was processed at the NY consulate (i think all TWP are processed only at NY). I am in CA and i sent all the passports to LA consulate since that is my nearest consulate.
We got the LOI (work permit approval) for my wife on May 7th and got the passport back after 2 days.
I got my LOI on May 15th and I am expecting my passport back by tomorrow.
Even though i submitted all the applications at the same time, my wife's and kid's applications were processed earlier than mine (not sure why).
So the entire process takes close to 3 months or a little more. There is no point in writing to NY consulate unless your application is more than 2 months. I have mailed twice and i got response for both my emails but i mailed them after 75 days. Hope this helps..