If the Ezekiel Anderson buried at the Cass, Michigan cemetary is the same Ezekiel Cole Anderson from Lawrence, Illinois, we may have a person to trace. If you can, try and find out how old E. Anderson was when he died in 1851. His age should be around 60yr to 63yr.
The marriage in Kentucky in 1815 and soldier status during 1812 would line up with a person born around 1788 to 1791. If this circumstantial scenario proves more likey then it is less likely that an Indian raid occurred in Lawrence, Illinois that is associated with E. Anderson's heritage. However, a more likely heritage would be one of a Native American being captured by White slave owning families in the Carolinas, of which both the Andersons and Coles are represented. I've always said that if slave reparations were actually realized, people would be surprised at how many Native American and White people would qualify for the awards. Several race conflicts between Cherokee and European settlers occurred during the timeframes mentioned. I would try to backtrack Ezekiel Cole Anderson from his marriage in Logan County, Kentucky and see if it returns to the Andersons in South Carolina, if it does,examine slave holding records of those families. Also, it appears that several "Goins" moved to the Negro settlement near Lawrenceville and are listed as "Colored." This still may be associated with the Melungeon culture.