Topsail Sound, Topsail Sound, Topsail Sound ------- not Topsail Island.
Well, that's what the Internet tells me. I don't know what locals call it.
If you are trying to use maps.google.com to find the routes, best to measure from Surf City NC (rather than Topsail Sound). Google-Earth knows about Topsail Sound but maps.google.com doesn't. Surf City is on the edge of Topsail Sound (within a mile), so a good proxy.
It looks like the best half-way point (driving or flying light aircraft) would be around Spartanburg SC or Greer SC. They are both about 310 miles from Carthage TN.