How about calling nearby Starwood properties (is there one at the airport?) and asking if you can store your bag without a reservation as a Platinum?

I've stored my bag before check-in at various properties just fine, so if you have some property you've been to in the past or will be staying at in the future they'd probably be more than happy to oblige... Of course, not as convenient as stashing your bag at the airport.

(And one could just make a fake reservation anywhere and store a bag, pick it up, then cancel, but that's a bit too much for my taste.)