I believe that your Battle line and our Williams line connect. Benjamin is the son of another Benjamin who was the son of a Thomas. The second Benjamin back was a brother to William Williams, and I believe father of my husband's 4th great grandfather Elisha Williams from Edgecombe, NC and then subsequently from Nashville, TN.
I'm happy to share what I have, though I don't have complete proofs for everything, though I have built a pretty extensive line going back to the death of John willliams who married Margaret Penny and died in 1733/34.
I never heard from other who have posted on this line, so hope you get this and are able to respond.