I think that it’s only those people who have taken on the mantle of “Traveller Returning” that can be said to have become Salt.
The rest are just zee-captains, yo.
Exactly. Your captain can’t become a part of Salt until you speak your burning name at last, sacrifice your mortal past, unravel all your fates, etc etc. Before that you’re trying to go east, but your personhood remains. No one goes east without a hole in the heart.
The FL player character can become linked with Salt in a way, if you decide to do something very very foolish.
No, the Captain aren’t any specific avatar of Salt, albeit the Burning Name involves at least partially losing part of you (or transforming yourself) as Salt did when he entered Neath.
All right, here it gets a bit spoilery on even Seeking ENDING - DON’T READ IF YOU DON’T WANT TO KNOW.
The goal of Salt isn’t going East, he merely had to go there to survive and finish the transformation. The Seeking Ending "Who is Salt" is bizarre as hell, but it leaves a lot of area to think what happened. What is know for sure is that entire Eaten or the Bazaar was part of the White, the Judgement Spymaster plan. Salt was send to Neath to save someone, but failed and succeed - he failed to save and succeed in survival. The White probably knew he would be destroyed in Neath. The ending itself states Salt thinking "They must know what White did."
Personaly I think it is connected to the Sunless Skies and Black Sun, but it still may be too little info to confirm that.