So...
(1) I only got the "we're out of space" call after I'd called Corporate. They weren't proactive on that.
(2) They apparently knew they were sold out circa 8pm but never cut off sales. Corporate had to intervene on that one and force them to cut off sales.
(3) Per the front desk at this hotel, there were multiple walks as a result. Not surprising, really, given all else...
(4) I didn't "talk the call center into" the redemption. The space was visible on the website for either cash or C&P. I just opted for a phone call.