There is a Westin hotel on Dawn Beach, and I heard they were selling timeshares. That's all I know about that.

You've mentioned the shoulder season a couple of times, and I'm pretty sure there are some La Vista Beach units available for that timeframe. Also, if I'm not mistaken, the two-bedroom units on the beach are lock-offs. I could be wrong about that, so be sure to check and make sure. (Which I'm sure you would, as you are being very thorough!)