Eric, I stopped in Lemont once about 15 years ago while driving past Chicago, and looked in a phone book, where there was still a number of Klings listed. I also found the little cemetary outside of town, and Rudy's gravestone, which has a picture of the SK-3 engraved on it.
Jim Harvey in St. Louis, who used to run the Monocoupe Club, has a number of photos of the SKs that I think he got from Clayton Folkerts, including some taken during construction if I remember right. He made me a set of copies, but I've long since lost track of where I put them. You might try to contact him through the current Monocoupe Club at monocoupe.com .
I used to know an old timer who flew a J-2 Cub to the Miami air races in '37, and said he was standing near Mrs. Kling when Rudy and Frank Haines crashed, said that he had a piece of the wreckage of the SK-3 for many years, but he never could find it while I knew him, and died a number of years ago.
Can't wait to see your replica.