It definitely hindered your search to go back generations on your paternal side, now that you have the correct James L Morgan, who went by the name of Layton on census records. I tried looking for your father's death certificate also, to no avail. But it could be the same type problem with the way enumerators/doctors reported, they used their own variations of spelling, hence the Leighton, Laton, Layton in census records on your grandfather. Some suggestions would be just to enter the surname Morgan in search for Birth Records, and his exact date of birth, limiting it to Knox, Laurel and Whitley counties ( I believe one child was born in Whitley, they moved often in a period of a decade or so). If that doesn't yield anything, the last name might be transcribed wrong like the Margan instead of Morgan, and all Kentucky birth records will only list child's name and mothers name maiden not married. So also try different variations of Vivian, like Vivianne, V.O., Viann, with Gibson, or Gibsun. Would your father had gone by his middle name Jerry and have a different first name? Gerald? It's trial and error. Last resort- is it possible that Layton and Vivian moved out of state in the 40's temporarily when they had your father? I will try looking myself more. One last thought, trying to search city directories in 1970's and after might help if your father lives in a metropolitan area, Cinn, OH, Lexington, Louisville or worked in one of those cities, or now if he lives out of state. I will continue to look also. Good Luck on your project.
The closest I could find on your Dad is an Ohio Birth Certificate that list the Father's name, only thing is Month is wrong. You can order it from vital statistics and it will list mother's name, etc. Closest I've seen to his date of birth you gave.
Jerry Morgan
Birth Date: 15 Dec 1948
State File Number: 1948173902
Additional Information: James