“Every day, a room would be a different color with new art on the walls,” Mr. Vinti said. “I’ve learned to go with the flow.”

In 2015, the theme was traveling. In April and May, they visited France, Germany, Hungary, Italy, Malta and Portugal. At each port of call, Mr. DelliCarpini expected to pop the question. But the timing never felt right.

“I didn’t want to stage it,” he said. “I wanted it to feel organic. And at every postcard spot, I couldn’t do it. I didn’t feel authentic. I was nervous. I never had the ring. I don’t like lying, and if he saw it, I wouldn’t know what to say. I wanted to recreate a moment we had in bed where we were talking and laughing and were so connected.”

In August, Mr. DelliCarpini was in Los Angeles for business, and Mr. Vinti joined him.

“It was my first time there,” Mr. Vinti said. “I’d taken a 4 a.m. flight and was so exhausted. All I wanted to do was sleep, but Gregory planned a day of sightseeing, and I didn’t want to let him down.”

That night, Mr. Vinti dozed off, and when he awoke, Mr. DelliCarpini was staring at him.

“While I was watching Lorenzo sleep, I got that same feeling when we were in New York and laughing in bed and were just so connected,” he said. “So I asked him to marry me.”