Crumble oven-dried bread into a large bowl. Add rice and saltines.
Cook sausage in a large skillet until it starts to brown. Add celery and onion and saute until transparent, 5 to 10 minutes. Pour over bread and rice mixture. Add stock and mix well. Add salt, pepper, sage, and poultry seasoning. Mix well. Add the beaten eggs and melted butter. Mix well. Reserve 2 tablespoons of the stuffing mixture for the Mushroom Giblet Gravy.
Pour stuffing into a greased pan and bake until cooked through and golden brown, about 45 minutes.
Bring stock and giblets to a boil. Add bouillon and reserved stuffing mixture. Make a slurry by whisking together the cornstarch and water and add to the boiling stock; cook 2 to 3 minutes. Meanwhile, saute mushrooms until browned in butter. Add mushrooms to gravy with egg and salt and pepper, to taste.