Thanks to experts on this forum, out trip to Argentina went fairly smoothly. Here is an update on the departure.

Tax: still $18 and they take credit cards!!!!!! It is pretty amazing for a cash based society.

For an AA coach pax without status, the check in process too over 35 minutes. It took a total of 1.5 hours to check-in, pay exit tax and got through immigration and primary security. For a continental coach pax, the total time is 30 minutes less. The entire check-in area was totally empty about 2.5 hours before the departure.