Heat oven to 375 degrees. Oil a 9-by-13-inch baking dish; set aside. In a large bowl, combine cornbread and rice, and set aside. In a large skillet, heat 5 tablespoons oil over medium-high heat. Add carrots, and saute until they begin to soften, about 2 minutes. Add onion and celery, and saute until onions are translucent, 8 to 10 minutes. Combine vegetables and bread mixture.
In same skillet, saute sausage over medium heat, stirring frequently with a wooden spoon to break up large pieces, until browned and cooked through, about 8 minutes. Remove sausage with slotted spoon; mix with cornbread mixture, along with poultry seasoning, sage, salt, and pepper. Discard rendered fat from skillet. Add stock, 1 cup at a time; mix. (You may not need all stock.) Stuffing should be well moistened.
Squeeze garlic from skins; mix gently into bread mixture; keep them whole. Season with salt and pepper. Transfer to prepared baking dish. Drizzle remaining 4 tablespoons oil over top of stuffing. Bake until top is golden and stuffing is heated through, 45 to 50 minutes.
To make ahead: Make recipe as directed. Cover well and refrigerate (up to 2 days ahead) or freeze if making farther ahead. Before baking, thaw, if needed. To reheat, bring to room temperature, and cover; bake at 350 degrees for 20 minutes. Remove cover; bake until heated through, about 10 minutes more.
**To roast the garlic, remove top quarter of bulbs, drizzle bulbs with olive oil, and bake 30 to 35 minutes.