score:3
Fast-forward two days >> So here is our experience at the Consolato Generale d'Italia in Miami. We went there with my wife and 1-year old child. We reached Miami 7:30 in the morning and went from there to the consulate. Our experience has been only positive. The staffs were highly accommodating given we were traveling with an infant. They asked us only the simple questions, and when asked about producing the long term visa document, I gave them my I797A Notice of Action, and they accepted it readily. Finally, we were ten-printed, and that's all. I am waiting for my Schengen visa in mail.
I hope my experience brings some hope to others who are in the same boat.