(picture to be inserted here later.)
Looking at it closely, I discovered that there was an older quilt used as the filling, or batting. My family did this a lot - once a quilt started getting holes or stains, it was put to good use as the inside layer of a new quilt.
Looking even closer, I could tell that the "new" backing had been quilted to the old one first, and then pieces added to the front. The first pieces to be put on were the edges. The last was in the center.
The "crazy quilt" patches were appliqued with a small running stitch (edges having been turned under), pretty much in the style of the original applique.
EXCEPT that I just found a similar block for sale on Etsy fo $25!