NEW YORK — Embargo lifts at 10 p.m. Sunday

The comedy “Some Like It Hot” would seem too hot to revisit these days. Easy laughs at the concept of men wearing dresses and then hitting on horrified other men? No thank you. Broadway — ever inclusive, forever progressive — would never touch that old, irredeemable chestnut, would it?

Gloriously it would, and in a musical no less, a big high-kicking, splashy show. And amid the scenes of ever-rushing gangsters, Art Deco set designs and rolling luggage carts, it’s been turned it into a sweet, full-hearted embrace of trans rights — a retelling that flips the original 63 year-old Billy Wilder film on its head.

The musical that opened Sunday at the Shubert Theatre captures the anarchic spirit and humor of the Tony Curtis-Jack Lemmon movie but takes it to a better place, somewhere previous men-in-dress shows like “Tootsie” and “Mrs. Doubtfire” were unable or unwilling to go.

It’s as if the creative team took to heart a lyric from the songwriters Marc Shaiman and Scott Wittman: “Perhaps it’s time to change the key/If where you’re at ain’t sounding great.”

Christian Borle and J. Harrison Ghee step into the shoes of Curtis and Lemon, two musician friends who disguise themselves as women and join an all-girl band to flee Chicago after witnessing a mob hit. Their comic timing is as perfect as their tapping.

And if the film “Some Like It Hot” made a star out of Marilyn Monroe, then the musical version has firmly announced the arrival of Adrianna Hicks in the Sugar role. “You were born for the close-up,” Hicks is told and she definitely is, sublimely belting “A Darker Shade of Blue” as well as wistfully singing “At the Old Majestic Nickel Matinee” and the mournful “Ride Out the Storm.” She also gets Monroe’s famous line: “I always get the fuzzy end of the lollipop.”

Book writers Matthew López and Amber Ruffin have moved the timing slightly up to the mid-1930s during Prohibition and the Great Depression and haven’t shied away from the implications that means for a multi-racial cast. “We headin’ south?” asks one member of the band. To which the Black impresario (an imperious NaTasha Yvette Williams) shoots back “It’s 1933. Look at me and ask that again.”

Shaiman and Wittman drench the score in ersatz Cab Calloway and Cole Porter, rarely leaving second gear and leaving the show without a big ol’ show-stopping title track. They even repurposed one of their old “Smash” songs — “Let’s Be Bad” — a remarkable piece of regifting because “Smash” also had a Monroe connection. The pair’s lyrics do much better, with “You Can’t Have Me (If You Don’t Have Him)” containing the lines “Can’t have Kipling without his ‘Kim’/You can’t have Depsy without the gym.”

Direction and choreography by a top-notch Casey Nicholaw is typical: Precise high-energy dances, crisp scene changes and romantic twirls, all presented with a knowing twinkle. He has created a farcical number with six rotating door frames that characters rush in and out of as well as tap-dancing chases, and a sweeping dance with a dozen performers featuring drill-team accuracy. Ukuleles go flying in this show. Couples do, too.

Scott Pask’s set designs deliver a sleek train, ever swirling cocktail tables, suitcases used as platforms for leaping dancers and a gleaming, ravishing Art Deco hotel. Costume designer Gregg Barnes elegantly dresses everyone from bellhops to the gangsters, swathing Hicks in sexy, shimmering satin.

The central conceit is still here: There are men in dresses trying to pass as women. But this time, the dress awakens something in Ghee’s Daphne. “I just feel more like myself than I have in all my life,” she says before launching into an anthem of self-discovery, “You Coulda Knocked Me Over With a Feather.” Being trans, we are told, is akin to the transformation from a caterpillar to a butterfly.

There are references throughout to the unfairness of society’s role for women in the 1930s (“No men?” asks one bandmember sarcastically. “But who’s gonna talk over us?”) One curious weapon the book writers have come up with to even the score and get men to listen to them is, well, scatting. Sometimes musical theater has its own magic, I guess. To steal a key line from the film that makes it to the musical, “nobody’s perfect.” Yet this show is very nearly that.