Eastern Taney County has a lot of Mark Twain National Forest land to choose from. Christian County, right next door to the east, is also loaded. There is also Drury-Mincy State Area, just a bit east and south of Branson. Contact or drop by an MDC office and talk with an Officer.
A little foot work and conversations with some folk, James River Archery in Springfield, can put you on the right path to find some good areas to scout.
Hope this helps.
PS-Never overlook talking with your local farmers, you just might be surprised who will not have a problem with giving permission for access to their land. Be respectful and responsible.
Good luck.