There's some misinformation here.
His UA works as follows : every barbarian ship spawns as either 'Convertible' or 'Not convertible'. If any Ottoman ship moves to a hex adjacent to a 'Convertible' barbarian ship, the barbarian ship instantly changes allegiance and grants the gold.
You don't have to end turn next to the ship.
You don't have to defeat the ship in combat.
Multiple ships moving next to it will have no effect, if the first ship to move adjacent to it does nothing, no others will do anything.
Multiple turns has no effect. Either you get the ship the first time you meet it, or you never will.
That said, my first (and only, so far) Deity win was Ottomans vs Greeks (randomed) on a duel Archipelago.
I got Sailing asap and sent a lone Trireme out amongst the 90% coastal waters. It didn't take long to find a barbarian camp on a tiny island, so I hung around it waiting for a ship to spawn. It did, and I lucked out, converting it. Then, I spread both ships out such that every water tile open and adjacent to the camp would also be adjacent to one of my 2 ships. Now I have my own ship-producing camp. Every time a ship spawns, either it instantly converts (because it spawns adjacent to one of my ships, which tags it) or my 2 ships combined kill it off in 1 or 2 turns.
My 3rd ship was sent out to locate another camp, which it then inhabited to start the process of a 2nd ship-producing camp. Soon, I had multiple camps sending out new ships like tendrils and my navy was spreading like a virus out of control.
My Capital was lazily creating a worker and happily producing a good amount of gold, which would turn out to be quite useful. I located the Greeks, they had 2 cities and a half dozen spots of open terrain on a tiny continent. My navy began to become a serious draw on resources, reducing my capital to 30% of its production output and starting to put me at negative income, though I had a reserve of about 1000g thanks to all the money from converted barbarians and capital surplus.
I took my whole navy and relocated it to camps which lay near the Greek island. I declared war, and the extra 10+ ships I had that weren't camping the camps destroyed the few greek ships that were about and began firing at the multitude of soldiers and workers milling about the island, while staying away from the 2 cities' range. The workers and warriors died easily, but it wasn't long before some Hoplites were roaming about, taking 0 damage from any attack. Clearly, I needed something other than a token land unit in order to conquer them.
Diverting part of my navy to form an escort from my capital, I brought up a Settler and managed to land it on one of the open tiles 4 hexes out from Sparta, thinking I could bombard any unit approaching it and use it to produce some land units to continue the conquering. Unfortunately, the Hoplites that approached still took 0-1 damage from most attacks, and they swarmed and took the city. Rats.
Thinking again, I thought maybe I could drop a citadel on their island, since I'd earned a few great generals from all the combat. Slowly hammering out another Settler, I escorted him and a general over to the area again. This time, I founded a city on a tiny island a few hexes away, then spent my dwindling gold to purchase 2 tiles across so I owned just a tip of the greek island, conveniently located behind a forested hill that the greek units wouldn't be able to cross and kill my helpless general before he could create the citadel. That's when things got amusing.
Apparently citadels work even when an opposing unit INHABITS the citadel, and I'm not sure if you can pillage them, but the AI wouldn't. So the Greeks started moving units into the citadel and embarking them in the water around it, where all of them would lose 3 hp every turn and eventually die. He suicided his whole army on that thing, and I never even had a unit inside it defending it. Meanwhile, my navy was becoming a drain I couldn't sustain, so I was slowly moving most of them to the little city I owned and deleting them.
Alex had asked for peace a few times already, first at terrible terms for me, then just straight out peace - but now, he offered Sparta itself as part of the deal, and I knew he was finished then. I accepted, and was able to continue my tech plan which involved getting to Riflemen asap. I maintained a watch around his remaining area to ensure that he could not spread settlers to anywhere new, and once I had my rifles (he was out-teched thanks to being unable to spread like deity insanity normally does) he died to the 2 upgraded land units I'd gotten.