Since I live in South Carolina I thought I would respond to your question about the rivers in SC. Yes, there is a Santee River that flows thru Georgetown and Charleston Counties in SC to the Atlantic Ocean. Also the Salt Catcher River flows thru Bamberg and Colleton Counties in SC to the Atlantic Ocean.
However I do not think that Francis was an overseer in South Carolina, but in Alabama instead. Francis was born in 1818 in South Carolina, but then the Wedgeworth families moved to Greene County, Alabama in the early 1820's. Francis' father, John Wedgeworth, died in Greene County, Alabama in 1824 and is buried in the Mount Zion Cemetery near Akron, AL. His tombstone is still intact there.
Francis probably worked as an overseer on one of his uncle's properties in Alabama before he married in 1843. Then he was off to Texas!
Hopefully, someone else will add more to the story.