Lovely, using the original draft script is hardly fair to prove your point, since over half of the things that happened in it did not occur in the movie.
Barbossa was going to shoot Liz, because he knew that Jack AND Will cared about her, and because she was in view. I don't think it's a deep, "Oooh, Jack loves Elizabeth moment".
It's a matter of plot-devicy moments all working together to make a fun ending for a fun character. 😄