This is the photo with the mystery date:In the photo above (you can click to enlarge and view details), Carl is on the far right. His collar suggests that the photo was taken before 1915, I think. Arden thinks it was taken in the mid-to-late 1920s. However, compare it to the following photo taken in the summer of 1930:
Although Arden thinks the top photo was taken between 1926 and 1930, it seems to me that, fashion aside, Carl looks significantly older in the bottom photo. His face has filled out, and seems to reflect the tragedies he's experienced in the previous 15 years. In the top photo he looks young, fresh-faced, full of promise.
I'm doing more fashion research to more accurately place the top photo, but my initial guess is that it was taken between 1910 and 1915. I'd love your input!