Okay I'm going to make some arguments.
Sparrow (ENTJ): Sparrow is a planner through and through, he only appears to be unpredictable due to his constant lying. His focus on the "opportune moment" in the first movie illustrates this pretty well. Sparrow has a drive to lead and also command which is characteristic of ETJ. He constantly exploits the trust, abilities and connections of his friends to the point where no one who has any personal goals will trust him anymore.
Barbosa(ESTJ)- Unlike sparrow, Barbosa's plans almost never involve the mobilization things external to his direct command. He is far more skilled than sparrow in the general operations of a ship and has a much better sense of what it takes practically to be a captain. He has a demonstrated command of the pirate code surpassing Sparrow at least. However for all his skill he lacks Sparrow's drive, Barbosa has no grand vision or plan beyond his current goals. He accomplishes his short term goals with vigor and dedication.
Elizabeth Swan (ExFP)- Throughout the films, her spirited outbursts of crowd rousing idealism are difficult to count, I think it figures in there around eight of ten. She is the ultimate idealist romantic. When she was in port royal her thoughts were only of the romance of the sea, and when she is at the sea her thoughts are still focused on the romantic ideal of piratehood. It's hard to gauge her N/S, I'm leaning towards S just because ENFPs I've known are incredible genuine, which she isn't really.
Turner is ISTP, you're right.
Norrington I'd still peg as F. He never really demonstrates any T, but shows tonnes of F.
Jones you're right too, INFJ.