Just before heading to the Great Smoky Mountains, where “Dirty Dancing” was being rehearsed and filmed in spring 2016, Mr. Johnson learned that the film was to be choreographed by Andy Blankenbuehler, who has won two Tonys for his work with Lin-Manuel Miranda, the creator of “Hamilton.” “I was like what?” Mr. Johnson said.

Several months earlier, the cast album of “Hamilton” had been released. Mr. Johnson — who won the state finals of a poetry-interpretation contest in high school and played in a college production of Mr. Miranda’s previous show, “In the Heights” — became obsessed: memorizing every word, posting videos of himself rapping the lyrics.

Throughout rehearsals, Mr. Johnson dropped hints about his love of “Hamilton” when in Mr. Blankenbuehler’s earshot and, less subtly, carried around with him “Hamilton: The Revolution,” the book written by Mr. Miranda, with Jeremy McCarter, including the music and an annotated libretto.

Amid the scene blocking, Mr. Johnson received a text from Mr. Linklater, who knew of his “Hamilton” fixation.

“Rick tells me he has a ticket for me to go to ‘Hamilton,’” Mr. Johnson recalled, “and I say, ‘Yes, let’s go, it’s on a Saturday and I’m not working.’ And then Andy Blankenbuehler is like, ‘Nope, I need you for a rehearsal,’ and I’m like, ‘Gee thanks, Andy Blankenbuehler, I thought you were cool!’”

After seeing “Hamilton” without Mr. Johnson, Mr. Linklater texted him: “Q you are definitely in this. This play has got your name all over it.”