Finally, the two artists worked together again on a hit sequel, “Bat Out of Hell II: Back Into Hell,” released in 1993. Meat Loaf continued to include Steinman’s songs on his albums like “Bat Out of Hell III: The Monster Is Loose” (2006), even as the two men waged a legal tug-of-war over the trademark rights to “Bat Out of Hell.”

Those disputes have since been buried, they say now. Mr. Steinman said in his interview that Meat Loaf “was my greatest muse,” describing him as “a rock ’n’ roll giant with an operatic voice.”

The road was now cleared for a “Bat Out of Hell” musical. In 2012, Michael Cohl, the veteran rock promoter, came on as a producer, and helped to hire its director, Mr. Scheib, a professor of theater at the Massachusetts Institute of Technology who is better known for his experimental, mixed-media stagings of drama, opera and ballet.

Mr. Scheib said he was attracted to “Bat Out of Hell” specifically because of its reputation as an unstageable work. “I’ve inherited a lot of impossible projects in my career, so that part made a lot of sense to me,” he said.

He felt that the musical’s “ginormous” book, about a pack of eternally youthful teens who live underneath a mythical city called Obsidian, needed some reshaping and paring down. But he felt a familiar connection between Mr. Steinman’s text and his music.

“The songs were straight extensions of the scenes,” Mr. Scheib said, “and they felt like opera scenes.” Besides, he added, “What better metaphor for a broken heart than a crashed motorcycle?”

The show found an equally unlikely leading man in the floppy-haired Andrew Polec, who plays its unruly protagonist, Strat, and who rushed to try out for the project when he learned about it at an open casting call for “SpongeBob SquarePants: The Broadway Musical.”