The shy engineer friend brought it to my attention that Sam Houston NF is just up the way from Houston, and not too far from the coast, and has regular camping, as well as dispersed.
https://www.fs.usda.gov/texas/
https://www.fs.usda.gov/activity/texas/recreation/camping-cabins
https://www.fs.usda.gov/texas/
https://www.fs.usda.gov/activity/texas/recreation/camping-cabins