I'm not familiar enough with the area to recommend a marina but I have sailed there a bit. You might want to expand your search to include Port St. Joe (Saint Joseph Bay) to the south or Freeport or Niceville to the west. I spent a week sailing around Saint Joseph Bay last summer in a Hobie 16. Really nice water and a nice steady sea breeze...
That expanded range should still be about an hour drive and you might have more luck finding what you are looking for.
You might also consider putting this request on the regional Craigs List... or use Active Captian to scout for marinas in that area....
For instance below is a screenshot of Active Captain marina listings for Panama City area... there is a lot of good info there regarding phone numbers and email addresses of marinas.
I'd write up a letter similar to the one you posted here and send it to each of the marinas in the area... see if anyplace allows for a "dry slip" situation (a boat mast up). I'm guessing you can find someplace that will work with you. Good luck.