We'd all have an easier time if my first mother in law was still alive, or I had a piece of an old Broken Stove quilt top to go by. As it is, all the clues (stovepipe wandering through the blocks, Tennessee) have been given. My memory is vivid of sitting with her outdoors on a lawn swing, piecing Nine-Patch blocks, talking about her quilting days. The swing was under an "ellum" tree as she called it--an elm to this city kid of 17. She was already white-haired at 65.
If the block cannot be found, and I can come up with my own design, it would honor her.
The picture of the Broken Block is intriguing and is downloaded into my Possibles folder.