The part that I made bold can't be true because just today our
travel agent changed our reservation from the AAA rate to the AP rate EXCEPT for the last day, which is the night of May 22, and it's all still on the same reservation #. In other words, we didn't have to book the AP rate days under one reservation and then the last day under a second reservation.
I'd call back and ask another CM. You should be able to at least get May 21st under the AP rate.
P.S. I just read that you don't yet have an AP; in this case, I don't think it'd be worth to purchase one just for the room discount, unless you're willing to change your dates. I, too, am surprised that the cut-off is May 21!