Saute chicken livers and sausage meat in 2 tablespoons oil until browned, about 6 minutes. Add remaining oil plus onion, pepper, celery, chili powder, salt and pepper and saute another 5-6 minutes until vegetables start to soften. Add broth and bay leaves and bring to a boil, scraping pan to loosen any browned bits on the bottom; reduce heat and simmer 5-6 minutes.
Add rice and stir well to combine, cooking until rice is heated through, another 5-6 minutes. Remove bay leaves.
Debone chicken by cutting up one side of the backbone and spreading carcass flat with breast side down. Find edge of carcass and carve out carefully, leaving as much meat as possible intact and skin uncut/unpunctured. Break leg joints at body and carve out thigh bones.
Stuff chicken with dirty rice, pull skin closed over rice, and truss with kitchen twine. Bake, covered, at 375 for about 45 minutes, then uncovered for 20-30 minutes more, until breast meat registers 165 degrees. Lift chicken out of pan.
Put pan over medium heat on burner and add 1 cup wine or broth to deglaze. Mix 1 tablespoon cornstarch with 3 tablespoons cold water to form a slurry; add to the pan and bring to a boil until thickened. Serve gravy with stuffed chicken.