Believe it or not their is a ton of turkeys in Central Louisiana. Kisatchie National forrest is the the largest public land in Louisiana and stretches as far south as Eunice,La. Here towards Woodworth and Alexandria there is not really a whole lot of pressure. Hope it helps. Good Luck hunting.
I use to hunt, with some success, on the Homochitto in the area of the Fox Road. This was 20+ years ago. Also the area north of 563. Haven't been there since then. I was on the forest on the Bunkley road this fall. There are some pretty woods on the forest there. Just don't know about the turkeys. You got to scout! I agree with you about the gobbling; I still 'hunt' them on my place just to hear them gobble and see them strut. Good luck!