|Captain Jones stood upon the forecastle of the Narcissus, (on would better suit the opening. Upon is a little ponderous)
out of ‘em. It was eternity (ellipses instead of a period would indicate a thoughtful pause in his tale and be a bit more 'haunting')
Clive stopped and slowly turned, like a ship coming about. (stopped and, turned to look back at Jeremiah. ?)
Must do so to keep up her crew, souls condemned to sail for eternity wi’out e’er seeing port.” (Must do so to keep up her crew. Souls condemned etc. ?)
The mist had become so thick, that Clive’s eyes were no longer visible. (had closed in so thickly that Clive's eyes were no longer visible. ?)
view by the milky haze of mist. (you already said it was so thick Clive's face was close to, if not, invisible. [...]by the thick haze of mist[...] or thick fog ?)
The smell increased in intensity and seemed to thicken in the muggy atmosphere (you might try odor or aroma in one or two of the places you are using 'smell')
the unmistakable gentle rushing sound of a hull (the unmistakable sound of ?)
The sound of the other ship’s hull, invisible through the mist, (passage ?came even with[...])
“God save us!” someone moaned a few stations back. Jeremiah wanted more than anything to cry out and give in to the terror, to run below decks and hide in the hold from the horrible thing which was passing by. Instead he gritted his teeth and pulled even harder. The Narcissus continued to creep forward under the weakening power of the men at the sweeps.
Very soon, the ominous sound of the other ship began to fade into the ship’s quarter. Jeremiah thought he imagined the horrible smell lessening, but soon it faded as well. His breath came easier, as if liberated from the choking wetness around him. The light of the moon seemed to rise a bit as the sound of the other ship faded away.
(these two paragraphs could be tightened up a little, I think)
Around them, the Narcissus slowly became visible as the mist evaporated. Jeremiah could see the Captain standing on the forecastle, his head tilted upward to gauge the visibility of the rigging above. (unless taking the place of the foreward lookout the Captain would most likely be at/on the quarterdeck or at the wheel. From there he could see the entire ship and the sails. )
Jeremiah didn’t answer. As the last of the mist faded away, the moonlight now shone fully on the still form on deck. (the sound of a body falling came from the hold. You might indicate the 'deck of the hold'. As written it reads as though Clive's body materialized on deck. On deck usually means the main deck of the ship under discussion)