Lin-Manuel Miranda and the cast of “Hamilton” perform at this year’s Tonys, where the hit musical won 11 awards. (Theo Wargo/Getty Images for Tony Awards Productions)

Lin-Manuel Miranda, star and creator of the Tony-winning smash hit “Hamilton,” says that he will leave the musical’s Broadway cast July 9 and that his longtime alternate, Javier Muñoz, will take over the role full time July 11.

In a breakfast meeting with reporters in the upper Manhattan neighborhood where he grew up, Miranda also said that the original cast — other members of which are expected to depart in the coming months — will film the musical later this month. But don’t expect the release of a “Hamilton” movie any time soon: Miranda says he wants as many people as possible to have the live experience of his Pulitzer-winning musical before it’s on any sort of screen.

Calling “Hamilton” “maybe the best idea I’ll ever have in my life,” Miranda defended the producers’ recent decision to raise the top ticket price to $849, saying it “pays for the second row of $10 seats.” The musical offers $10 tickets in the front of the orchestra via a daily online lottery.

In the wide-ranging conversation — joined by Miranda’s father, Luis, and an exuberant Muñoz — the actor-composer gave a portrait of life inside the whirlwind into which “Hamilton” has swept him up, and detailed some of his other projects. He will soon begin work with actress Emily Blunt (and with his fairly untested British accent) on Disney’s sequel to “Mary Poppins” with a score by “Hairspray’s” Marc Shaiman and Scott Wittman, in which he plays a London lamplighter. And he has completed his contributions to the score of a new Disney animated movie, “Moana,” set for release this fall.

Even so, Miranda’s relationship will go on with the musical that has brought him a level of fame and success that he says is still hard to completely process. He says he hopes to return to the role of Alexander Hamilton from time to time, and he’s even open to the possibility of jumping into touring incarnations of the show “when a Hamilton needs a vacation.” A “Hamilton” will begin performances in Chicago this fall for an open-ended run. And a separate touring production that begins in Los Angeles in spring 2017 will visit the Kennedy Center in summer 2018.

“I think this is a role I’m going to come back to again and again,” he said.

Being invited to a meeting these days with MacArthur “genius” grant winner Miranda feels a little like getting a summons from a prince — although, to quote Cinderella in Stephen Sondheim’s “Into the Woods”: “He’s a very nice prince.” Among Miranda’s latest endeavors is a merchandising venture launched this week at teerico.com for Miranda-related, and not completely “Hamilton”-centric, items. The first offering is a T-shirt bearing the words of the sonnet he read Sunday night in his acceptance speech for the Tony for best score. (He also won for best book of a musical.) The proceeds from the T-shirt sale, he said, will be donated in memory of the victims of the Orlando nightclub massacre, through Equality Florida, a gay rights organization.

“Hamilton” Inc., it seems, is just starting to get rolling. There’s a 90-minute, independently produced documentary, “Hamilton’s America,” that will be broadcast Oct. 17 on PBS. It will include interviews with President Obama and former president George W. Bush as well as with Sondheim and John Weidman, who collaborated on several history-based musicals, including “Pacific Overtures” and “Assassins.” The director, Alex Horwitz, has been shooting footage since the show’s earliest days. “He’s got filming of me writing ‘My Shot,’ ” the composer said of one of “Hamilton’s” most popular songs.

Miranda also said he plans to be politically active this fall. Although he hasn’t been recruited for a role in a presidential campaign, the actor, of Puerto Rican heritage, says he wants to make sure his community’s voice is heard loudly in November: “I’m going to try to get out the Latino vote as hard as possible.”

Muñoz, meanwhile, says that he’s ready to move up to the No. 1 slot in the show and that he’s recovered from the cancer he was diagnosed with last year. “Fit and ready” were the words he used for the seven-performance-a-week assignment. (A new alternate Alexander Hamilton will now be cast, Miranda said.)

As for plans for another musical, Miranda says he needs to catch his breath, which is often the most productive time for him. The idea for “Hamilton,” he noted, came to him while on vacation. “When I get a moment’s rest, I’ll know what the next one is,” he said.