Well ... just for kicks, I tried this one more time tonight and pulled up the information on spg.com. And wouldn't you know that this property now has many openings -- various rooms at 5 or 6 different rates -- for the night I needed. So I cancelled the Four Points res and re-booked the Sheraton—at the original low (AAA) rate I had originally reserved.
It makes me wonder what happened here. Just 3 or 4 days ago, the manager on duty told me the hotel was "nearly full," and that she couldn't rebook me at my low rate because the going price was a best-available or rack rate of around $200. She also said I only received the lower rate because I had booked it a month or more in advance, and now it was too late to get something that low. A group must have pulled its reservations, or perhaps one of the events in town was cancelled. Either way, I got to spend some quality time on the award-winning Starwood site tonight.

It was even slower than usual tonight, so much so that I almost gave up.