I also have an unsolved Minor/er family line, so I thought I'd try seeing where your line led to in case there might be a clue to mine. I first looked at the US Census listings without much help, but when I went to the Public Trees onAncestry.com, I found your lineage.It traces to Joseph Minor and Mary Hoskins who came to Kentucky from Virginia after the Rev. War in which Joseph was a veteran.I would say the genealogy work looks probably accurate to that point.The parents to Joseph Minor are, in my mind, questionable as stated on various family trees in which he is listed.Some say his parents are William Minor and Frances Phillips of Green Co. PA which I think cannot be correct.Ohters say his parents were Joseph Minor and Edith Cox of Lunenburg Co. VA which may be correct, but there is a question on that. Your Joseph Minor married Mary Hoskins, but there is a question as to whether the Joseph, son of Joseph and Edith, married Mary Hoskins or was it someone else. The Joseph Minor of Lunenburg Co. VA traces his ancestry to the Minor family who settled in Westmoreland Co. VAin the 1600's.
If you go to the Public Trees at Ancestry.com and find those that have Joe Lee Minor in them, you will find a number of fellow genealogists who are researching, or who have researched your Minor lineage.You may also find these Public Trees on www.rootweb.com if you are not a member of Ancestry.com.That is their free website. (I have not checked that out, but I do know they duplicate the Message Board.)