Okay, let's see how it could work, from James' perspective, a quick day-by-day:
Day 0: James wakes at sun rise. Everything happens as in canon, except while they start planning on getting Elizabeth back, directly before sun rise, James is suddenly in his bed again
Day 1: James wakes up at Sunrise. As noone says anything, he assumes it was all a bad dream. Everything happens as the day before, but when proposing to Elizabeth, he steers clear from the wall and has an eye on her. When he sees that she looks ill, he asks if she is okay. As a result, she faints in his arms. He still doesn't get an answer, but at least the woman he loves didn't fall into the sea. The rest of the day is peaceful, there is no attack. James goes to bed almost having forgotten the "nightmare" from the first day.
Day 2: James wakes up at Sunrise, going for the day as if everything is normal and is very confused when people bring up the ceremony for the promotion. He's steered their bemusedly against his intent, goes through with it a bit absent-mindedly and is in such a daze he doesn't propose to Elizabeth afterwards. She doesn't go to the wall alone, but faints in front of him. He doesn't catch her in time and she hurts her head. The rest of the day us worrying about Elizabeth, being confused and meeting with his subordinates about things he could have sworn they discussed already
Day 3: James wakes, hopes for a moment everything was a dream, but can predict his staff. He skips breakfast, goes to the church and prays for guidance. He's collected for the ceremony and draws it out by repeatedly not doing anything until someone prompts hum, leading to worried questions about his health. After the ceremony he considers proposing to Elizabeth again when he's interrupted by a marine informing him that a pirate sailed into port on a mask and stole a ship of middeling size. By the time they arrive at port, the ship is over the horizon. James still orders to prepare the Inceptor to follow it, even though most people don't think it worth it. They leave a few hours later, but find no trace of the stolen boat until Sunrise
Day 4: James is prepared and delays the ceremony to capture the arriving Jack Sparrow. He declares to the bemused pirate that he will be hanged the next day, ignoring the pirates comments that the next day won't come, then locks him up and goes to the ceremony, during which Elizabeth faints. He manages to catch her, delays the ceremony again to get her taken care of, and finally is made Commodore. The rest of the day he spends very efficiently planning, using his previous experience
Day 5: a bit desperate, upon waking up again, he repeats the previous days, ignoring Jack's constant pleas for a parlay, and his obvious attempts to explain that they're both caught in the time loop
Day 6: this time, he orders Jack hanged immediately, even before the ceremony. It doesn't help
Day 7: he shoots Jack on sight. The rest of the day is chaos
Day 8-20: Jack does not show up again, or at least not to James' information; after a few days he stops asking. He concentrates instead on his proposal, starting of by sending a message to the Governor that he's worried about tight-lacing. After two attempts he manages a message that has (bemused) success, and the proposal goes through without Elizabeth fainting. She still doesn't say yes but asks for time to think about it (as if she hadn't known he would propose). He spends several days desperately changing up his proposak, without success, before he gives up and instead tries to ask her about what she wants. What she wants, he finds out, though not directly, is Will Turner. The next day he doesn't get out of bed.
Day 21: after being declared sick and left alone in bed, he's surprised by Jack climbing through his window. An argument ensues, but Jack escapes before he can arrest or kill him. His doctor is very worried about his hallucinations
Day 22-30: he tries to go through with the day again, but starts collecting additional information by doing things slightly differently every time, and talking long with different people. His communications with Elizabeth are short and stiff. The second he's alone, he's always ambushed by Jack and they get in a very unproductive argument, where Jack just wants them to team up
Day 31: James gives up and gets drunk with Jack. He doesn't remember the rest of the day
Day 32-60: Jack stops ambushing him, but starts increasingly daring stunts, among them stealing every single ship in the port separately, and gaslighting marines into helping them. Whenever James shows up, they have increasingly flirtatious shouting matches (on James side. Jack's flirting was top notch from day one), which James does start to enjoy, as he is getting very bored (and depressed) by everyone else always being the same and even starting to get over Elizabeth. Their banters start becoming a bit staged, as both are aware that there's no real consequences (though dying hurts, as Jack complains. James does not try to kill him again)
Day 61: during their usual confrontation, James kisses Jack, shocking everone around him and himself. Jack grabs his hand and they flee together into a house whose owners are not there for the day, as Jack ensured in the past. They have sex. Then they agree that the best way to figure out what is going on is to repeat the first day exactly, Jack promises to rescue Elizabeth again. They have sex again
Day 62: James tries to go through with the day as in the original, but panicks when Elizabeth falls over the wall, follows her, falls, too, but unfortunately does not miss the rocks, breaks his neck and dies
Day 63: James manages to repeat day one, but Jack breaks character by demanding to speak with James before he takes his hand. He takes him into his office, where Jack kisses him. He's extremely shook by pulling James' corps out of the ocean the previous iteration. Also, the black pearl arrived the previous day, and Jack, claiming to be a relative of James and not being arrested, managed to sneak on board and find out that the pirates were very interested in the coin of Elizabeth, and Elizabeth herself when she claimed herself Turner. They also are definitely cursed (that, they knew already) and it stands to reason the two curses are connected. They try to get further protection around the governor's house, knowing that the pirates will come for the coin& Elizabeth, but everyone is cut down and the black pearl sails of with Elizabeth and without them. They plan a meeting & planning session the next day, and calculate where they can meet before midday
Day 64: James gets up early, takes a boat and sails off with basically no explanation, to an island Jack can reach with his leaking boat before it's just a sail. They start planning, but decide they need a) the coin and b) the map for further plans. In the mean time Jack suggests a steamy vacation, it's not as if there's consequences
Day 65-70 James tries to find the coin in sleeping Elizabeth's bedroom without waking her (feeling very conflicted about it), but has very little time. He is caught twice and decides both times to run away instead of dealing with the consequences. The other days he goes through the motions, researches the isle de muerta and everything connected, and meets up with Jack in the afternoon
Day 71: James manages to steal the coin, and gets away with a boat to meet Jack. The dip the coin in the ocean and then have another vacation on their island. When the black pearl arrives there, they tell Barbossa that James is James Turner and promise to come in peace (threatening to throw the coin in the ocean) unless they get to know the whole story, at which point they realise they need Will Turner's blood, and also the location of the isla de muerta, which they will each long after sunrise the next day, so they fail
Day 72-80 they try to find a spot to be picked up faster by the black pearl, but still are never able to reach the black pearl, so back to the drawing board: they try to triangulate the location of the island, together with Jack's knowledge, and sail to find it themselves, hut the time is not enough
Day 81-100: James starts stealing the Interceptor to go looking for the Isla de Muerta, together with the marines on watch, who are roped into it. They get closer.
Day 101: James steals the coin again, hoping it will help him get to the Isla. He isn't careful enough and wakes Elizabeth, who is immediately on board with the whole adventure, especially if they get Will, and manages to get Will on board in record time. They steal the Interceptor with the three of them, kidnapping the two marines
Day 102-105: James perfects dealing with Elizabeth in the morning
Day 106: James immediately goes to wake Elizabeth in the morning, saying exactly enough to get her quickly on board, they collect Will, kidnap the Interceptor with guarding marines and sail towards the usla de muerta, picking up Jack in his sailboat on the way. They reach it about half an hour before sunrise, find the treasure, and drop the coin with Will's blood in just seconds before sunrise. It works, time passes and they go outside to celebrate in joy as they see their first new sunrise in quite a while. They kiss. Then they have to figure out how to deal with the aftermath, which includes the probably now uncursed but still not in Jack's possession bkack pearl, James kidnapping the Governor's daughter (and some random people) for several days instead of going to his ceremony, and a lot of feelings. But I'm sure they'll figure it out...