How this chaotic miracle comes together is the work of Mr. Coulton, Mr. Sabourin and Greg DiCostanzo, who is the “Storm” of Paul and Storm, and Drew Westphal, the chief operating officer of the partnership. Mr. Sabourin and I met to talk in the ship’s casino, a place we knew would be quiet. In a lounge across the way, the JoCo planners set up more than 40 vintage video game consoles, which drew a crowd day and night. On the casino side, the dealers had nothing to do. “Everybody here actually understands probability,” Mr. Sabourin joked.

These folks haven’t always had an entire ship to themselves. The first cruise attracted about 350 Coulton fans. It’s grown, year by year until three years ago they were able to book a ship. This year, the ship sold out. Next year’s cruise, on an even bigger ship, is selling out fast. No cruise yet has lost money, Mr. Sabourin said.

To Mr. Sabourin, the cruise is not just a job — in fact, a multimillion-dollar-enterprise — and exhausting fun, but also a mission. The organizers seek a diverse cast of performers and passengers. The cruise also raised some $80,000 for Puerto Rico after 2017’s devastating Hurricane Maria.

“We’re helping bring people joy, helping them learn new things and getting them out of their comfort zone,” Mr. Sabourin said. “I want people to be better for having attended this event. Maybe that sounds lofty from someone who writes humorous music for a living, or incongruous for an event happening on a giant floating hotel. But I stand by it.”

To the brink of disaster

The third night of the cruise started with an L.G.B.T.-friendly dance party on the open deck of the ship as it slipped out of the pier at Tortola. The mood was light, and the D.J., Riz Rollins, spun songs with his husband, Rob Green. Before his first cruise last year, he said, he’d expected a very white crowd, given the reputation of nerds, but was pleased to encounter a more diverse group. “I didn’t know what a ‘blerd’ was until the cruise,” he said, using the portmanteau term for black nerds. He marveled, too, at the degree to which the JoCo culture is participatory. “It’s the first time I ever saw people dance — to karaoke.”

The next night was supposed to be the biggest show of the trip, an outdoor concert in a San Juan, P.R., park after a day wandering the city. The lineup included well-known performers like Aimee Mann and Jill Sobule, and the headliners were They Might Be Giants. (Ms. Mann, a Grammy-winning singer-songwriter who is anything but nerdy, said in an interview that “It’s not really my crowd, but Jonathan encompasses a lot of different things under his umbrella.”)