I have very little to help you other than one distant fact from my own family. A Thomas Hart, aged 3, appears in the Arkansas Federal Census of 1850, living in the household of J C Duncan and his wife, Lucretia in Crittenden, Arkansas. Between 1850 and 1860, Lucinda Duncan (my g-g-g-grandmother) came to Missouri with several of her children and Thomas Hart. He shows up in the 1860 Federal census for Madison County, Mo., still living with Lucretia.
Lucretia and her children obviously settled in Madison County, Missouri, just north of Farmington, Missouri. I have no idea what relationship Thomas was to my Duncan relatives, but I have been searching for a Thomas Hart in that general area for about a year, to see if it reveals information about Lucretia.
In the 1870 census a Thomas Hart (b. 1847) shows up in Bollinger County, married to a young woman named Mary. Bollinger County is just south of Madison County.
Possibly your father could be descended from this man. Long shot, but sometimes the most random facts turn out to be helpful.