This looks like a sampler quilt I made many years ago as a class to make a quilt as you go quilt. It was done using the
Georgia Bonesteel method. It was a great method. As for the missing square you could make one that is similar to those you have, or, you could write the story of the quilt, put it on a fabric square you can run through the printer (maybe use a photo or two) and put it into the quilt. The blocks are lovely and the story touching.