John, Thank you for the photo.The reason for the single birth date for William Johnson Washburn is that he remarried after Abbie's death.He died in 1933 in Valparaiso, IN.If you want more on this story, I will send it to you privately, but since you are not a Washburn you probably won't want it.
William C. Washburn, son of Hezekiah Washburn, had Abbie's birth as Feb 2, 1847 - which is close to Feb 4th per tombstone.The story about naming Hezekiah Washburn after Hezekiah Vermillion appears to be true - at least that is the story in the Washburn family line.
The March 23, 1847 birthdate for Hezekiah Vermillion that I have came from Wayne Vermillion.In the 1860 census of Bracken Co. KY (page 043, Augusta township) shows Abbie as 14 years old and Hezekiah as 13 years old.Yet in the 1880 Bracken Co., KY census; Hezekiah (head of household) is 33 years old and separately Abbie, wife of William Washburn, is shown as 33 years old.I have no other source of Hezekiah's birth.
By the way, in the descent line you have shown above, didn't you leave out Albert V. (son of HezekiahV.) as the father of Clyde Nelson V.?