Billed as “The/King/Operetta,” the scattershot new musical by the touted young theater company Waterwell actually sports a much longer title, “The Last Year in the Life of the Reverend Dr. Martin Luther King, Jr., as Devised by Waterwell: A Rock Operetta.”

Lengthy titles, grandiose pronouncements, and eyebrow-raising musicalizations have become summer-theater staples over the last decade, thanks to the Fringe Festival. And this latest entry by the prolific Waterwell, which has made its name by creating musicals collaboratively, embraces many of that festival’s smirkier, less desirable qualities. A restless theatrical imagination and a sincere respect for Martin Luther King can be spotted deep under the collegiate antics, but the company’s irony-rich diet blends uneasily with the unadorned eloquence of its subject matter.

After a bratty bit of powerpop (“He’s the greatest/Of the Greatest/In the greatest land/In the greatest universe/And he’s the subject/Of the greatest show of all”), “The/King/Operetta” kicks off with the iconic preacher’s hugely influential speech “Beyond Vietnam,” which he delivered on April 4, 1967 — one year to the day before his assassination.

It was here that King (played by Rodney Gardiner) publicly expanded his focus from defending civil rights to denouncing A merican involvement in Vietnam, and its parallels to 21st-century global affairs undoubtedly had as much to do with Waterwell’s decision as the speech’s eerie timing. The Vietnamese people, he said, “must see Americans as strange liberators, as we increase our troop commitments in support of governments which are singularly corrupt, inept, and without popular support.”

This abrupt shift in tactics squandered a large portion of the goodwill that King had accrued nationwide, and the ensuing year saw increased paranoia from the White House, discord within his own organization, the controversial adoption of a Poor People’s Campaign, and a second march on Washington before his fateful trip to Memphis. On April 3, as part of his support for the city’s 1,300 striking sanitation workers, he delivered “I’ve Been to the Mountaintop,” a speech that would live on in the annals of American rhetoric even if King had not been assassinated the very next evening.

The “Beyond Vietnam” and “I’ve Been to the Mountaintop” speeches are by far the play’s longest and most straightforward passages. They are also, by an equally wide margin, its most effective. Mr. Gardiner gets the little things right—the lingering caress of the final consonants in his sentences, the studied stillness of his hand gestures — but he also captures the quieter moments elsewhere in “The/King/Operetta,” as when King mediates among squabbling staffers or sinks deep within himself during a late-night interview.

Unfortunately, the view from King’s oratorical mountaintop is cheapened by its tawdry, anything for-a-giggle surroundings. Waterwell pokes simplistic fun at clueless hippies, a drunken talkshow host (the versatile Hanna Cheek, who also plays a long-suffering Coretta Scott King and even, hailing back to her journalist days, a cynical Joan Didion), and, in the case of President Lyndon Johnson (Arian Moayed) and J. Edgar Hoover (Kevin Townley), buffoonish villainy. As directed by Tom Ridgely, these sequences generate their share of broad laughs — Ms. Cheek is a scream as the TV host who responds to King’s Vietnam request by blaming an unwanted pregnancy on “unilateral withdrawal.” But they come in lieu of any sort of reasoned examination of what King’s words meant to a divided nation.

They also, almost without exception, rely on absurdly easy targets. Given this penchant for cheap laughs, the only shock generated at the sight of J. Edgar Hoover in an evening gown and elbow-length satin gloves comes from the fact that Waterwell managed to hold out for 75 whole minutes before drawing upon this shopworn image.

The snickering abates when King and his coterie of activists hash out strategy and enjoy one another’s company. One of the play’s few truly successful blends of historical import and cheeky irreverence comes in a jaunty duet for King and Ralph Abernathy (Mr. Ridgely) as they welcome a brief jail sentence as a respite:

Five days ain’t no sentence;
One week ain’t no time.
My only chance to catch my breath
Is when I’m convicted of a crime.

Composer Lauren Cregor roams freely within the period, using an insistent 1960s soul sound as a framework and expanding it to include gospel, blues, and even a tentative (and rather misguided) stab at minstrelsy. But despite having a burnished baritone voice reminiscent of Otis Redding’s, Mr. Gardiner fares better when forgoing Ms. Cregor’s score and finding the music in King’s actual speeches.

Those speeches, which bookend “The/King/Operetta,” are as stirring an argument as you’ll find for Martin Luther King’s qualification as “the greatest of the greatest.” But how meaningful can that designation be when your only competition is cartoonish perfidy, cartoonish naivete, or cartoonish ignorance?

Until August 11 (27 Barrow St. at Seventh Avenue South, 212-239-6200).