Looking for a mysterious 3rd-great-grandfather

The third of my research questions for the current DNA study group is to identify a third-great-grandfather on my Mom's side of the tree, the father of Mary Alice Cain Read. My strategy at the moment is to use my Mom's DNA matches, and create networks of people descending from best known matches from her Read/Holsclaw line, Flatt/Gaw line, and Whitley/Matthews line. I already had a Read/Cain group based on matches from my 2nd-great-grandparents Charles Read and Mary Alice. This is about 2900 matches.

I created a group called "Cain Targets" and assigned everyone from the Read/Cain group who did not match to Flatt/Gaw, Read/Holsclaw or Whitley/Matthews to that group, creating a network of about 1900 matches. I know there are still some matches to those lines in that network.

Next I took anyone who had a common ancestor with one of those three lines, and unchecked any of their matches, then unchecked themselves from the Cain Target group. I repeated this step until there were no more matches with common ancestors on these lines. This brought the total to 1731, which is still a lot.

I'm now in the stage of looking at the matches who have connected trees, and checking to see who has descendants in their tree who were living in Barren, Metcalfe or Adair County, Kentucky between the 1850s and 1880. Then I'm going to look at those groups to see if I can identify any patterns of names. After that, there's more steps to learn from the DNA study group to see what can be done with this group of mystery matches.

This strategy might not work. There's already the complication that Nancy Jane Flatt's second husband was also her first cousin. There's also the possibility that this could work and topple the brick wall on this side of the tree.