To update you all, I checked out this morning and the front desk agent added my SPG number to my folio. She did mention the stay would post as 0 points because of the third-party booking. (All I really care for is a record of this stay under my account.) She was extremely courteous and graceful, per Starwood tradition.

I also learned (from a non-Starwood source) a reason for the night agent's tergiversation. Only a selection of rooms are visible to the front desk, and it may very well have been that all such rooms were occupied, so to walk-in guests the hotel was truly sold out. But the front desk cannot see, nor book, a room if it was among the block of 20 on HotelTonight.