You can try Harry's http://www.placencia.com/members/harrys.html
We reserved a cabana a few weeks ago. Harry's friend does his online reservations for him. Since he doesn't do a lot of online marketing, and you are arriving Wed, you might have a chance there. They definitely had room when we reserved ours. We'll be in the cabana with the stove.
I've heard a lot of nice things about Harry's, so we're going to try it. It's right in town, on the south end. It's less than $50USD/night.