Not something I have paid too much attention to, I have seen cases where needing something from the Consulate was required, as I said I had assumed this was the exception, live and learn.
Hmm now admittedly not something I have ever looked in but I would have been going from the opposite assumption as far as a document from the Consulate is concerned. Just goes to show.
Work Authorisation seems to be coming through in a few months, Advanced Parole is still taking time.
If you stay and adjust you will get a Green Car not a visa.