Friends - thought I'll post the resolution.
Sent my passport and pertinent documents via VFS Mumbai on Monday morning. On Friday morning got an email saying my passport was ready and would be couriered. Received the passport on Saturday afternoon (note, consulate was closed for a day). The new visa stamp reflected both 797s.
Reached New York Monday morning and guess what - the immigration officer did not even look at my 797(s). He saw my visa stamp, asked me where I worked, and stamped my visa and i-94. So all worked well in the end.
Thank you all for your responses.
Adi