Grayton Beach around Thanksgiving

Any one have any experience with the availability of sites at Grayton Beach, FL over the Thanksgiving holiday period? DW & I are thinking of trying that this year, but have a few things that might hinder the trip and won't be resolved until the last day or so, so reservations are out of the question.
Ultimately we like to spend about a week there and then work our way over to Gulf Shores and then back to ST. Louis. Camp out of a B and only require electric and nice facilities. Any suggestions/recommendations?