Maria Friedman’s rethinking of the much-loved, much-monkeyed-with 1981 Sondheim-Furth flop gets very close to coherence, and all the way to enjoyable.Many people love something about “Merrily We Roll Along” but few people love everything.It has that brilliant Stephen Sondheim score! It has that meshuga George Furth book! It’s a comedy of misbehavior, a tragedy of cynicism, a big Broadway musical, a tiny domestic drama, a timeline in search of a story that’s never found and, anyway, doesn’t make sense. Even if it did, no one is old enough/young enough to convincingly perform roles that age in reverse from 40 to 20. And if they do, they can’t sing.What no one wants is to leave the 1981 flop alone. Though too often lifeless in its many incarnations, it is also somehow deathless, rising repeatedly from the glossy grave of its beloved original cast album — remembered more fondly than the messy if emotional original production — in hopes of a transfiguration that finally makes it work.The revival that opened on Monday at New York Theater Workshop, after earlier iterations at the Menier Chocolate Factory in London and the Huntington Theater Company in Boston, comes closer to meeting that goal than any of the many I’ve seen before. Maria Friedman’s staging brings the intelligence of the songs fully alive and justifies the baroque construction. Her framing snaps the picture almost fully into focus. And with Jonathan Groff, Daniel Radcliffe and Lindsay Mendez as the show’s central trio of backward-tumbling friends, it is perhaps for the first time perfectly cast.Is that enough to make it great, the way it never was?The question resonates with the material — which, being about show business, is always involved in a meta-conversation with itself. Groff plays Franklin Shepard, a hacky movie producer in 1976, trailing two wives with a third on the way, who gradually evolves (backward) into a promising theater composer in 1957. Radcliffe plays his word man, Charley Kringas, who, in a nationally televised meltdown in 1973, spectacularly splits from the oldest of his old friends. Mendez plays the third wheel, Mary Flynn, an embittered (what else?) theater critic and washed-up novelist whose fog of alcohol slowly burns away to reveal, by the final curtain, a hopeful innocent in love forever with the unavailable Frank.Groff as Franklin Shepard, who’s a hacky movie producer when the musical opens in 1976.Sara KrulwichFriedman clarifies this rangy structure from the first image, which replaces the ensemble scenes of previous productions with Frank standing completely alone in the ruins of his life. As disembodied voices sing the opening phrases of the upbeat title song we quickly understand that we will be focusing not on the triangle so much as its apex. No one else in the story, not even his besties and exes, is quite real to Frank anyway; they are props in his monodrama, and often mangled. This is going to be the story of a brilliant young man who, failing to grow up, inevitably punches down.Happily, Groff has the glamour and fury to shoulder that interpretation. No Frank I’ve seen has been so unapologetic in his solipsism, so sure he deserves a get-out-of-jail-free card to life’s every complication. And when someone crosses him, as Charley does singing “Franklin Shepard, Inc.” on that TV show, Frank is so livid, staring straight ahead as if his friend no longer exists, that you wait in terror for what will happen next. What you get, even worse, is what happens before.The laminated ironies of Furth’s timeline, lifted from a 1934 Kaufman and Hart play with the same title and a similar arc, have always seemed better integrated into Sondheim’s ingenious score than into the plot itself. The songs are structured like a musical in reverse, with reprises preceding instead of following fuller versions, and bits of accompaniment later revealing themselves as new melodies. By the time you hear “Our Time,” the exquisite hymn of hopefulness that ends the show, you will recognize that it has already been cannibalized for parts; a few of its bleached bones show up as early as the second number, “That Frank,” with much more cynical lyrics.Friedman’s staging for the first time raises the story to nearly the same level of expressiveness. The dialogue, which in most productions sounds like movie lines instead of actual speech, has been put through some sort of sanding machine that removes its polish and restores real texture. Even in the songs, phrases that can seem too perfectly crafted are now engorged with specifics that inform the actors’ delivery and thus our understanding. For “Franklin Shepard, Inc.,” Radcliffe seems to have written a Bible of back story, giving wild spins to every line that help send the song into orbit.Visually too, Friedman simplifies, reinforces and focuses what we see. Soutra Gilmour’s costumes, though changing with the years, are similar enough to immediately specify everyone in the cast. (Frank is usually in a black suit, Charley in eye-jarring argyle, Mary in busy print shmattes.) And since all the action takes place within the cold unit set representing Frank’s midcentury Bel Air house (also by Gilmour) we never wonder why we’re watching a scene, even if it nominally takes place somewhere else. We’re watching it because it’s his brain.From left: Reg Rogers and Krystal Joy Brown, with Groff, Mendez and Radcliffe.Sara KrulwichBut those fixes, however successful, are also compromises. The Bel Air house, fairly hideous and mostly blank to allow for its transformations, necessitates a lot of choral furniture-handling that works against the sleekness of the material. Though the cast, especially Mendez, is vocally splendid, the original Jonathan Tunick orchestrations, vastly reduced to nine players from 19, have undergone a radical deglamorization, making it a smart if sad choice to drop most of the brilliant overture. And if dancing doesn’t really fit Friedman’s more interior approach (the limited choreography is by Tim Jackson) the general lack of Broadway pizazz leaves the show feeling deprived of half its inheritance.With the Off Broadway run (through Jan. 22) all but sold out, and commercial producers teed up for a transfer, we may yet find out what “Merrily” can be at its best. For now, it’s just at its best so far. That means some scenes work as they never have; the Act II opener, “It’s a Hit,” which often lays an egg, is for the first time hilarious, thanks in large part to Reg Rogers as Frank and Charlie’s producer. The unlikely progress through the story of Gussie Carnegie — the producer’s secretary, then wife, then star, then ex, but in reverse — suddenly seems clear and, in Krystal Joy Brown’s fetching performance, charming if not credible.Yet at the same time, some things that used to work no longer do. The supporting characters, heavily doubled, are mostly a blur. The song “Old Friends,” which at its root is about the fatal compromises that keep people together, has a case of fake giddiness. And “Bobby and Jackie and Jack,” a comedy number about the Kennedy family that the three friends perform in a downtown club in 1960, lays the egg that “It’s a Hit” no longer does.Musicals are mysterious. Even the best are games of Whac-a-Mole: Fix one problem and another pops up. It’s therefore no small thing to say that in her effort to drag a half-living thing like “Merrily” to full life, Friedman is more than halfway there. Maybe, finally, it’s a hit.Merrily We Roll AlongThrough Jan. 22 at New York Theater Workshop, Manhattan; nytw.org. Running time: 2 hours 30 minutes. More