I like your suggestion . . . except, I wonder how the date could be durably, and easily applied to the items. I can't think of a method that takes very little (essentially zero) time or maintenance, but is available to every/any participant. If one wraps each piece in layers of paper (time consuming) the item would be easy to date mark and protection might be enhanced, but I'm certain that the item would be separated from its dated wrapping after one or two subsequent participants unwrapped it to view the item. I think it would boil down to too much trouble (not following the process).
I just thought of a possible solution. Every participant takes a picture of his contributions, prints an 8.5" x 11" of the image and writes the date on it. The sheet is placed into a sheet protector and put in the box. Can everybody take a photo? Can/will everybody print it 8.5" x 11" (B&W would be OK)? Who's got a sheet protector to contribute? It's the easiest way I can think of but I don't expect it would be universally adhered to.