Just got back from the Circle M antler auction in Iowa and they had a shed like that in a booth. I think he called it a shared base shed. He told me they have a category for this in the record books and his was number 4 in the world. Yours look bigger than the one he had, so it may go high in the record book. I don't know if there is a category or not, I am just relaying information. It may be worth looking into. Maybe someone else can confirm this.
Great find, Congratulations. I'm sure it's a pretty rare find.