Growing up in Poplar Bluff, we had some awesome neighbors. One in particular, Granny Sielert, was more like family than just a friend. I was going through some of my mom's old recipes and found one that I hadn't seen before, it is titled "Granny Sierlert's applesauce cake". You can tell it is an old time one, by the use of lard instead of butter or shortening. The recipe, like a lot of old recipes, took a bit of deciphering, but this is it. Sounds like it would be a good one.
Mix together 2 cups unsweetened applesauce with 2 teaspoons baking soda and set aside.
Mix together in a large bowl, 3 cups flour, 1 tsp cinnamon, 2 tsp. cocoa powder, and 1 tsp. salt.