I am beginning to see where the confusion is. I was hoping you had documentation I have not seen showing Henry Coffman also went by John Henry Coffman. The Coffman's 1812 War application for land you reference is listed as Henry Coffman and all pages following have his name is listed as Henry Coffman (not John Henry Coffman). I have gone through each page.
Also, I have a copy of Abraham Coffman's will. As you have pointed out above, he does not have a son listed as John Henry Coffman. (FYI, the A. Miller that you could not make out the name was Axsa (Coffman) Miller who was married to John Miller and I believe they died in Illinois.
Please let me know if you do find documents that list his name as John Henry and not Henry.