NEW YORK — As producers of substantial Broadway hits often do, those responsible for “The Band’s Visit,” winner in June of 10 Tony Awards, asked critics to return to the show recently to sample the performance of a new leading cast member. In this case, it was Sasson Gabay, an Israeli actor who has assumed the role, in this musical of longing and loneliness in a dried-out place, of an Egyptian conductor named Tewfiq, marooned with his orchestra in the wrong Israeli town.

Instead, I found my gaze drawn to an actress in a smaller role, Kristen Sieh — and she’s been in the show since its inception off-Broadway in 2016.

What distracted me from the appointed task had only tangentially to do with Gabay, who starred in the 2007 movie version on which composer David Yazbek and book writer Itamar Moses based the musical. Gabay, making his Broadway debut in the role Tony Shalhoub originated on stage and for which he earned a Tony, is a commendable successor, although one feels as if, like a new tenant, he’s still settling into strange digs, only just now beginning to treat it like home.

Which takes me back to Sieh and the other 16 actors and musicians who share the stage with Gabay, and together nightly build the world of Bet Hatikva, a town filled with souls tested not so much by tumultuous human events as ones seemingly hardly worth mentioning. While it is on Tony winner Katrina Lenk, as Dina, that the accidental visit of the Alexandria Ceremonial Police Orchestra has the most direct emotional impact, the changes wrought by its presence have sizable consequences for others all over town. Like Sieh’s Iris. She’s a deeply unhappy woman, married to a sweet but childlike man, John Cariani’s endearingly well-etched Itzik. And in the few short scenes she gets — not even the length of a song — Sieh has to reveal to us a whole character, and with that the depth of Iris’s caged despair, the anger she experiences at a spouse who seems unwilling to grow up.

This Sieh accomplishes, poignantly, and, against the undertow of Itzik’s innocent charm, without turning Iris into a drudge, or a villain.

Her performance made me think about an idea “The Band’s Visit” conveys. Under rocks in the desert, you sometimes find surprising signs of life, and so it can happen, too, in the drab brick apartment blocks of a desert town like Bet Hatikva.

It also reminded me how, over a long run, a musical doesn’t have to sit still. In this fourth trip to director David Cromer’s production, I had what felt like the most moving visit to Bet Hatikva yet. Many of the actors have been together for more than 300 performances at the Ethel Barrymore Theatre, and many date back to workshops and the off-Broadway run. The experience shows, because the portrayals affect you even more deeply. When, for instance, Andrew Polk, as Iris’s father Avrum, breaks into Yazbek’s exuberant memory song, “The Beat of Your Heart,” the moment he’s memorializing — meeting his late wife — exudes a greater heart-pounding joy now. (He’s egged on expertly in the number by Cariani, George Abud’s Camal and Alok Tewari’s Simon.)

The timing of the humor in Moses’s script — a Pinteresque love of the pause abounds here — has been upgraded to Swiss. And no relationship now pays off more enjoyably than that between Etai Benson’s sullen Papi and Ari’el Stachel’s rakish Haled. The evening in a Bet Hatikva roller rink, where Haled tags along behind Papi on his foundering date with Julia (Rachel Prather), is a blissful mini-musical unto itself. Benson sings to Haled the hilarious “Papi Hears the Ocean,” about his inadequacy with women, a number that sounds as if “Habanera” from Bizet’s “Carmen” is being sung in a panic. Then Stachel replies with his liquid, jazz-inflected lesson in an almost spiritual kind of seduction, “Haled’s Song About Love.” And the scene is completed with Papi accepting Haled’s gift of guidance — an Egyptian leading a Jew to his romantic destiny.

Like Sieh, and for that matter, Adam Kantor, playing a young man waiting for days by a pay phone for his lover to call, and singing the beautiful “Answer Me,” Benson and Stachel are exemplars of an extraordinary ensemble. Right this minute, “The Band’s Visit” may be the best it will ever be.

The Band’s Visit, music and lyrics by David Yazbek; book by Itamar Moses. Directed by David Cromer. $49-$299. At Ethel Barrymore Theatre, 243 W. 47th St., New York. or 212-239-6200.