Those folks setting the mortar on the concrete pad, lifting it with the "eye" were taking a chance. No one I know who is knowledgeable regarding cast iron mortars, would consider lifting it with the eye, especially on a mortar that old. The cast iron can break off with all that weight on it. Sure the eye was designed for lifting the tube only, but they have tube and bed suspended by the eye.
Regarding the differing appearance of bore and the rest, it makes sense considering that all the US 13" mortars were cast using the Rodman casting process of internal cooling, then boring the bore up to the required diameter. The iron in the bore area is denser than that in the remainder of the mortar, due to the compression of the surrounding molten iron during cooling. It would seem that the denser iron would have different corrosion characteristics, but I have no facts to back up that theory.