Point: The buoyant force is equal to the weight of the water the object displaces. You cannot calculate it using the pressure equation as you have written. If the entire volume of the object has been submerged then the buoyant force on the object is where V is the volume of the object and is the density of water.
Question: What are you defining buoyant pressure as? If I am not mistaken the buoyant pressure is the difference in pressure between the top and bottom of the object (if both surfaces are parallel and horizontal.) Please correct me if that isn't the definition you are using.