One goofier nonetheless more compelling challenges on skill-based reality-TV contests such as “Top Chef” and “Project Runway” involves the alchemical kick of making something really good out of something really bad. Couture created from a recycling plant, haute cuisine reinventions of franks and beans — that sort of thing.

And so it almost goes with “Xanadu,” in which a number of seasoned Broadway pros simultaneously mock, embrace, deconstruct, and tart up with surprisingly agreeable flair the excruciating 1980 roller-disco movie of the same name.

There are a few crucial differences. For one thing, the Broadway incarnation requires more time (albeit not much more) and more money (quite a bit more) than an idle Wednesday in front of the tube. For another, the participants — among them the resourceful director Christopher Ashley, the marvelously catty playwright Douglas Carter Beane, and a chamber-size passel of gifted comic actors — have taken on this Sisyphean task voluntarily.

Their efforts have been trained on source material that, even in the era of “Hot Feet” and “Urban Cowboy,” stands out as questionable. Judging from an informal poll, most people have seen the film — starring Olivia Newton-John as a roller-skating muse and Gene Kelly as a fedora-wearing clarinetist — once. A few have seen it dozens of times. There is no middle ground. (And, yes, those two categories slot fairly dependably depending on a few key demographics. Okay, on one key demographic.)

Many people, however, have heard “Xanadu,” thanks to the hit-filled Electric Light Orchestra soundtrack. Jeff Lynne, aka the least-recognizable member of the Traveling Wilburys, contributed a battery of songs that blended the sinuous melodies of Burt Bacharach with a disco beat that was tailor-made for the roller rink. By augmenting this collection with a handful of other E.L.O. tunes, Messrs. Beane and Ashley have combined two much-maligned Broadway trends: the movie adaptation and what one character calls “the musical of the box that is juke.”

That odd syntax warrants an explanation. “Xanadu” is about not just a muse but an actual Muse — one of the nine Greek sisters who used their demigodliness to inspire the arts. (Owing to budget concerns, the number has been winnowed down to seven, two of them played by men.) Mr. Beane has followed this fact to its semilogical theatrical conclusion and constructed a daffy forbidden romance in the stiff, archaic style of most mid-20th-century English translations of Greek drama.

In this telling, Clio/Kira (Kerry Butler) falls for the dim mortal named Sonny Malone (Cheyenne Jackson) at the malevolent coaxing of her sisters Melpomene (Mary Testa) and Calliope (Jackie Hoffman). These two Hellenic hellions cite envy of their adorable younger sister as the reason for their transgression; judging from the amount of scenery chewed by the two, however, gluttony is the more appropriate vice.

Early on, Mr. Beane’s high-low collision relies heavily on bottom-feeding interpolations of slang along the lines of “He my baby daddy” and “Oh, snap!” He seems to grow more and more confident in the rightness of his approach, though, as the story becomes less and less comprehensible. (A working knowledge of “Clash of the Titans” comes in handy by the end, as does a tolerance for satin short-shorts.)

Ms. Butler’s near-perfect take on Kira has a lot to do with this added comfort level. Ms. Newton-John’s Australian accent was about as appropriate for a Greek muse as it was for a bobby-soxer at Rydell High School, one of many incongruities that Messrs. Beane and Ashley exploit mercilessly. Ms. Butler’s approximation of her predecessor is viciously adept: She somehow stuffs every single vowel into the word “go,” thins out her redoubtable voice to replicate Ms. Newton-John’s watery upper register, and conveys a singular unease whenever on her ubiquitous roller skates. Both in on the joke and completely in tune with Kira’s burgeoning humanity, Ms. Butler pushes past the leg warmers and wooden dance moves to unveil a real character.

Mr. Jackson, an eleventh-hour replacement, manages the near-impossible and turns the vapid Sonny into a charismatic, even adorable romantic foil. And in the role of Danny Maguire, a wealthy businessman who fell for Kira decades earlier, Tony Roberts proves a good sport with his absurd material despite opting out of the more physically taxing sequences.

Mr. Ashley, who knows his way around cult favorites (“The Rocky Horror Show”) as well as wiseacre deconstructions (the Wagnergoes-Nashville “Das Barbecu”), has a deep fondness for the defiant frivolities of camp. Rather than attempt to equal the film’s ridiculously elaborate musical sequences, he shrewdly plunks an array of zero-budget tricks into the action. And when that fails, he and Mr. Beane have a secret weapon — or rather a pair of secret weapons, as the formidable Ms. Testa and the rubber-jawed Ms. Hoffman are allotted several stretches of brassy, borderline unhinged, frequently inspired shtick.

Most of the cast members — although, sadly, not Mr. Roberts — spend a decent portion of the show whizzing around the tiny stage in roller skates. (At a recent performance, nearly one-third of the tiny cast was on the injured list.) Making this even riskier is the presence of a few dozen audience members sprinkled around the stage, along with musical director Eric Stern and his tiny but potent orchestra, which does a remarkable job replicating E.L.O.’s synth-drenched sound with just four musicians.

It is among this slightly dazed crowd that the inessential and ludicrous pleasures of “Xanadu” pile up. At one point, Ms. Hoffman’s conniving Calliope finds herself hiding behind a few of them as she and Melpomene hatch their plan: “Cackling and hiding, listen to us. This is like children’s theater for 40-year-old gay people.” She said it, not me.

Open run (240 W. 44th St., between Broadway and Eighth Avenue, 212-239-6200).