Just an update on this for anyone who is planning to do this. It is still largely the same as mentioned in the original post.
I went this morning (Thursday December 22) - arrived around 8am. Took the commuter train from the Mitre Station in Palermo to Retiro - quicker and cheaper than Subte if you are close to the station.
Two lines out front. I went to the "Citas Turnos" line which was the one on the right. I did not have to say anything to get in when I walked to the front, but the person at gate was checking many who did. Once inside, you walk through one of two security portals to another line. In this one, the person at the front asked what I was there for. I showed my US passport and said "prorroga". He asked if I had the 4000 pesos in cash and checked the date of expiration on my visa (must be within 10 days of the end date) before letting me through.
At the next window on the right, they did some initial processing for my extension and gave me a ticket for the booth section on the other side of the room that does the actual extensions. I waited at a seat before someone came to get me.
At the booth, I completed a form with my passport info and my residential address in Argentina. The person asked for my profession, my home city, and my marital status. She took my photo and also my fingerprints for both hands. I signed a number of forms. I was given a form to take to the Caja window in the next room/building to pay the 4000 pesos. I returned with the receipt. After some more processing including scanning every page of my passport with any information, I was given the receipt back, my passport back (nothing was stamped inside), and given a piece of paper with instruction on getting the "Prorroga Turista" online at their website.
The whole process took less than an hour at that time of the day.