Lost Sitting Bull Cabin

I am trying to track down the actual physical location of Sitting Bull's cabin. Thus far, I have tracked it to the Columbian Exposition in 1893. I have contacted the Smithsonian and the Chicago Field Museum hoping to get some leads as to where it ended up. Here is an NPR "Dakota Datebook" story about the cabin going to Chicago.
http://www.prairiepublic.org/programs/datebook/bydate/06/1206/120306.jsp