OK, one possibility: Take I-49 at Shreveport, then pick up I-10 at Layfayette to I-12 in Baton Rouge. There are two nice state parks just off I-12: Fairview Riverside at Madisonville and Fontainbleau just down the road at Madeville. I know there are some private parks in the same area but we have never stayed at them. In recent years we have favored Faiview Riverside.
It should be an easy trip from there on down to Destin.
We have also stayed at Buccaneer State Park near Waveland, MS.
EDIT TO ADD: If these are two far down the road for "half way" there are some good parks around Lafayette. I can't remember the names just now as we are on the road, but they should be easy to find.
