States: Georgia: Gilmer
The 1880 Gilmer Co, GA census does include a Francis J. Watkins and a couple of the sons you mentioned ... I'll send you exact details via email. I have not been able to connect them with any of the other Watkins families in Gilmer at that time.
Sorry, but Watkins Memorial was the Methodist church in Ellijay; believe I recall reading that it is being replaced by new church which will be called First Methodist. Hospital in Ellijay was also named Watkins Memorial; it is now the North Georgia Medical Center. Both church and hospital were originally named after families of Dr. Ed W. Watkins, Sr., and Dr. Ed W. Watkins, Jr., whose monetary contributions made the construction possible.