Two e-mail responses I recieved from Elite Services that clarify the rules of this promotion.
Dear HepperSchepp,
Any stays that post to your account during the promotion dates should count toward the promotion. Unlike past promotions in which it had be a paid stay, if your first stay is a redemption stay it should count as your first stay and any additional stays will earn double points.
AND
Dear HepperSchepp,
As long as you check in to your stay before September 15, and have a
previous stay, you should earn double points for your stay. Be sure to
check on your account after your stay, if you do not see the double
points, please contact us.