Primitive? Go to Padre Island National Seashore. You have 65 miles of beach, seldom a camper within a mile of you, and burn a fire as big as you want. Collecting firewood there is ok. Just don't burn treated wood which washes up on shore, it releases the chemicals into the air and smell nasty. It is a good place to get away from it all, just need a 4x4.
This would be quite a drive for you. What about somewhere in a neighboring state? Maybe their rules for primitive/no ground fires would be different, especially if they've had rain. Good luck.