Combine first 5 ingredients and, if desired, sugar in a large bowl. Stir together 2 eggs and buttermilk; add to dry ingredients, stirring just until moistened.
Heat bacon drippings in a 10-inch cast-iron skillet or 9-inch round cakepan in oven at 425° for 5 minutes. Stir hot drippings into batter. Pour batter into hot skillet.
Bake at 425° for 25 minutes or until cornbread is golden; cool and crumble. Freeze in large heavy-duty zip-top plastic bag up to 1 month, if desired. Thaw in refrigerator.
Melt 1/2 cup butter in a large skillet over medium heat; add green onions and celery, and saute until tender.
Stir together remaining 4 eggs in a large bowl; stir in cornbread, onion mixture, stuffing mix, and chicken broth until blended.
Spoon dressing into 1 lightly greased 13- x 9-inch baking dish and 1 lightly greased 9-inch square baking dish. Cover and freeze up to 3 months, if desired; thaw in refrigerator 8 hours.
Place 13- x 9-inch dish (uncovered) and 9-inch square dish (uncovered) in oven at 350°. Bake 13- x 9-inch dish for 1 hour and 9-inch square dish for 50 minutes or until each is lightly browned.