Yes, I believe we are related. My Great Grandfather was George P Miller who was the first born (of 8) of John W and Sarah Rather. He was born in 1854 and had a younger brother named Noah Anthony born in April 1865. I am in regular contact with Robert Miller, a descendent of another of their brothers Belvely Clark A Miller, the last of the children, who was born in 1869 and was the closest in age to Noah Anthony. I'm in California but visited that area of Kentucky this past May and spent some time in the genealogical center there. I found the grave of James M Rather who was the father of Sarah Rather and that line goes way back. At this point no one is certain who the parents of John W are, even though we have investigated and can speculate including the William you mention or another named Samuel but have not been able to document. There were more than one Miller family in the area at that time. I have a photo of John W and story of his military involvement if you are interested. Of course I have also visited John & Sarah' grave site in Missouri, where my parents were born. I can me contacted directly by email at email@example.com. Feel free to write.