I was at the Eden Roc for 3 nights for a conference last week. I didn't book a room, it is now in their slow season. I knew they wouldn't be full and I knew I'd be able to negotiate better at the front desk. I told them that I had a room booked at the Marriott and that they would have to give me an awesome deal to stay. The conference rate was $269, so they kept the rate the same, but gave me a high floor ocean front suite, free breakfast ($38. per day) and free valet parking ($42 per day).
You just need to negotiate with leverage. If they would have told me to pound sand I would have walked and stayed at the Marriott and collected my points.