For at least half of “See What I Wanna See,” Michael John LaChiusa has put his money – well, the Public Theater’s money – where his mouth is.

After storming onto the off-Broadway scene with “First Lady Suite” and “Hello Again” in the early 1990s, Mr. LaChiusa found a large bull’s-eye on his chest when the now-defunct Theater-Week magazine put him on the cover with the headline “The Next Sondheim?” (Disclosure: I wrote the story, although not the headline.) He then managed to get two defiantly uncompromising musicals, “The Wild Party” and “Marie Christine,” on Broadway in the same season, only to see them both underperform commercially. But things came to a head earlier this year, when he publicly accused some current Broadway hit makers of creating synthetic “faux-musicals” instead of art.

Each of these has earned him his share of detractors. And ill-conceived works like “Little Fish” and “The Petrified Prince” haven’t helped his case: He’s far more prolific than many of his peers, and quantity sometimes overwhelms quality. But when Mr. LaChiusa’s on – and he is very much on in “Gloryday,” the transcendent final portion of “See What I Wanna See” – he delivers an object lesson that audiences can be challenged as well as invigorated. It is the first exploration of the post-9/11 American psyche in musical theater, but it’s not likely to be bested in its cathartic power. It only barely redeems the spotty vignettes that precede it, but “Gloryday” will be remembered as a major work for a long, long time.

“See What I Wanna See” has been billed somewhat misleadingly as a modern-day gloss on the “Rashomon” tale, best known to Western audiences through Akira Kurosawa’s 1950 film, which famously showed the malleable and ultimately unknowable nature of truth. In fact, only one of the evening’s three pieces deals with “Rashomon,” although the other two are also adapted from stories by Ryunosuke Akutagawa (translated here by Takashi Kojima). Mr. LaChiusa has set most of the first act, a shady noir pastiche called “R shomon,” against the premiere of Kurosawa’s film.

As in the film, three accounts of a murky sex crime elicit three very different “truths,” filled here with knife fights and dangerous dames in tight red dresses. The participants this time are a lounge singer (Idina Menzel), her oafish husband (Marc Kudisch, whose gifts as a singing actor grow more and more impressive) and a street tough (Aaron Lohr) who lures them into Central Park late one night.

For all the louche torch songs and plot machinations, staged cleanly but unexceptionally by the respected musical director Ted Sperling, the “Rashomon” homage doesn’t add up to much. The final message is that “truth” is subjective and hinges on the teller. Everyone sees what they wanna see. Well, we already knew that, through the Kurosawa and dozens of other treatments. Where do you go with that? What does the individual teller’s story say about his or her truth? Why do we tell this story and not that one? Any exploration of “Rashomon” needs to tackle these questions.

But Mr. LaChiusa – whose “Hello Again” updated another fragmentary classic, “La Ronde” – and Mr. Sperling are content to merely unspool the different versions. It’s all recapitulation and no resolution, albeit depicted with a remarkably crisp aesthetic. (At the risk of hyperbole, I would suggest that Christopher Akerlind does stage lighting as well as anyone does anything in the theater right now.)

All three versions paint the teller in a particularly unflattering light, a state of perceived iniquity that pervades Mr. LaChiusa’s far more ambitious “Gloryday.” “They cry for absolution,” says a disenchanted priest (the stirring Henry Stram) burdened by the world’s misery. “As if they’d know what to do with it, if they had it.” Mr. LaChiusa and Mr. Sperling rise to the occasion in chronicling his fall and rise, glutting the stage with a heightened sense of anxiety as well as hope.

In the wake of an unnamed calamity clearly meant to evoke that “bright blue crisp blue day” in 2001, the priest plants the rumor of a pending miracle in Central Park as a cynical joke. Sure enough, the masses converge (“Battered wives, dying boys, / Hungry souls, the worst of men / Along with the good”) and the priest is caught up in their shimmering potential despite himself. His impious act ends up bringing him – and, for a time, everyone from an off-the-grid CPA (Mr. Kudisch) to a coked-up actress (Ms. Menzel) – closer to God. Even his atheist aunt (Ms. Testa) admits to a lifelong twinge of faith, or as she memorably describes it, “there was always something scratching inside the walls.” Simple in structure, joyous in execution, “Gloryday” harnesses the narrative force of great short fiction to the harmonic joys of great musical theater.

Some singers take to Mr. LaChiusa’s astringent, cresting style more readily than others. Mr. Lohr’s swaggering hoodlum in “R shomon” gives the impression of a boy trying to imitate his tough older brother (picture “Rebel Without a Cause” with Sal Mineo in the James Dean role), his work in “Gloryday” is only slightly more comfortable. Mr. Stram’s slight frame is well suited to his characters, even if he strains slightly in his upper vocal register. And Mr. Kudisch (the best thing in Mr. LaChiusa’s “Wild Party”) and Ms. Testa (one of the best things in his “Marie Christine” and the recent “First Lady Suite” revival) have Mr. LaChiusa’s style down cold. Everything about the show – the staging, the harmonies, even the book – improves with their haunting duet in the first act, and they are even stronger in “Gloryday.”

Ms. Menzel, by far the biggest name in the show through her tween-friendly roles in “Rent” and “Wicked,” is hit-and-miss; her formidable, pop drenched vocal stylings sometimes amplify and sometimes overwhelm the score, which draws heavily from the dusky jazz of the period in “R shomon.” Mr. LaChiusa’s published screed earlier this year alluded to Ms. Menzel “holler[ing] an incomprehensible power-ballad,” in “Wicked.” Power ballads are nowhere to be found in “See What I Wanna See,” but the same can’t always be said about the hollering.

She and Mr. Kudisch open each act with the show’s clearest nod to its Japanese origins, a he-said-she-said vignette between two adulterous lovers. Mr. LaChiusa uses the same insinuating melody each time, reminiscent of a similarly themed song in “Hello Again”; it is appealing when Ms. Menzel sings it and then sublime when Mr. Kudisch does. This escalation in ambition and execution parallels the two longer works in “See What I Wanna See.” What starts out as a derivative curiosity explodes into a major step forward for Mr. LaChiusa, who instead of pointing out the missteps of others (undeservedly in some cases) has created a ravishing path of his own.

Until December 4 (425 Lafayette Street, 212-260-2400).