The Chattanooga bike club has reserved rooms for the 3S3M riders at the Marriott near the start of the ride. They have posted a group discount code that will get you a room for $95.00. I recommend calling the Marriott to make a reservation rather than trying to reserve a room online. The online system may tell you there are no rooms available if you want one for two nights and it will not give you the discount for both nights. However, the Marriott gave me the discounted room for both nights when I called them and said I was coming for 3S3M.
You can call the Marriott at 1-423-756-0002. The Staybridge also said they were full, but you may try to call anyway.