John McCully was the oldest of six brothers who are thought to have served in the Missouri Confederate service. Most lived in Randolph and Howard county but John and brother Michael relocated to Schuyler County, Mo about 1854 with their families. The first names you mention are not known descendants of John or Michael McCully. Your family could be related to one of the other brothers. Do you know of ancestors previous to your Harold McCully? Perhaps we can tie them in that way.
You may contact me at firstname.lastname@example.org if you wish. I am happy to help if I can.