Richard,
I too have relatives that started in Georgia and rode via covered wagons to Alabama and boarded a vessel they referred to as the "Little Mayflower" and took it around the Gulf of Mexico where they then boarded another vessel that took them up the Sabine river to Jefferson, Texas.All this taking place around 1875. My relatives then took a wagon to Dalton,Texas which is close to Marietta,Tx the birth place of my father. I have not been able to find any information on the "Little Mayflower", but a lot of vessels were probably renamed. I am looking into one that changed it's name to "Silvie" . Good luck with your search.