You are right, 4 or 5 letters aren't really much to go by. So a different derivation may well be possible. From HINTS to HINCE there is only one little step, so why not.
Now the spelling Hince isn't German, this would be HINZ, and Hince would be an adoption to English. I case the ancestors were German indeed, they may have come across the English name HINCE (see above) and changed the spelling of their name (maybe because they wanted to preserve the TS-sound, at least roughly).
So we would have to ask Charlotte, whether she can find out more about her (?) ancestors.