As long as we’ve had democracy, we’ve needed argument to make it work. Those long-ago Athenians voted only after discussion in the Assembly; democratic theory has always held that good choices emerge from intellectual combat. So, it’s relevant to ask—how is that going? In two current shows in New York, the theatre weighs in on the usefulness of political argument: a deliberately astringent Broadway staging of the musical “1776” looks askance at our nation’s founding conversation, and the Off Broadway play “Baldwin and Buckley at Cambridge” makes the whole confrontational mechanism of debate seem suspect. In both, we watch as crucial issues—in a way, the same issue—are erased and avoided by rhetoric. Persuasion feels impossible, and the public dialogue sounds corrupt. At least the language sings.

It’s a tricky thing to revive Sherman Edwards and Peter Stone’s 1969 musical, which originally starred a congress of white guys (surely the appropriate collective noun) in breeches. John Adams, Thomas Jefferson, Ben Franklin, John Dickinson, et al. hector one another in sweaty Philadelphia over whether to declare independence, and the climax—a victory of compromise over ideals—comes when Jefferson is persuaded to remove a condemnation of slavery from the Declaration. (Dramatically, that peak is a dud; historically, it could hardly matter more.) Only two women get to say anything at all: Abigail Adams, who writes to her husband to keep his spirits up, and Martha Jefferson, who inspires her husband’s, ah, quill. There’s enough nostalgic love for the show (the 1972 movie was shown in U.S. history classes for a while) that many in the theatre have wanted to “solve” it. A color-blind, modern-dress 2016 Encores! production roused affections but also stumbled over conceptual problems created by, for instance, a Black actress playing Martha. The Sally Hemings issue, literally, cannot stop cropping up.

The directors of the current version, Diane Paulus and Jeffrey L. Page (who is also the show’s choreographer), address the musical’s awkward optics and gender inequities by casting it with a diverse group of female, nonbinary, and trans performers, in addition to adding some stern looks whenever the hypocrisy—Jefferson talking about equality—gets too much. Crystal Lucas-Perry plays Adams with a rueful sense of command, sighing, “By God, I have had this Congress,” with a complex expression of weariness; this attitude is how the production, per Paulus, intends to “hold history as a predicament versus a confirming myth.” A predicament it certainly is, particularly since the production at the American Airlines Theatre—accidentally?—suggests that even changing the makeup of our governing body results in the same injustices, the same horse-trading and moral capitulation. Otherwise, the adjustments to the underlying musical seem modest: arrangements for some songs emphasize the choral; one of the dorkier numbers (“The Egg”) now rocks out; and the creators have added lines from a real Abigail Adams letter in which she admonishes John to “remember the ladies.” The casting causes some quite lovely musical changes, too—for instance, Abigail (Allyson Kaye Daniel) and John’s duets, reset for two women’s voices, are newly lush and gracious.

The creative team is using a cross between the strategies of Lin-Manuel Miranda’s “Hamilton,” which famously cast white Founding Fathers with Black and brown performers, and Daniel Fish’s realist staging of “Oklahoma!,” in which characters registered the violence in the script and slowed the show’s tempo, dampening the general state-founding glee. Crucially, though, the Edwards-Stone musical hasn’t got the same bones as these two musical-theatre landmarks. “Hamilton” was applying its diversifying methods to every part of itself, including its creation and sound; in “Oklahoma!,” the source material already contained a rich vein of doubt about cowboy ethics. How do these two techniques—recasting and ironizing—deal with “1776”? Well, when it comes to casting as critique, our own power to suspend disbelief takes over after only a few minutes. Spend only a scene with Patrena Murray as Ben Franklin and you adjust, so the subversion of the actor’s identity quickly subsides. As for the stern looks, the more annoyed the company grows, the stranger it gets. A tart glance is one thing, but long glares at the audience, performed by the ensemble, can turn unintentionally funny. They seem so mad about performing this show they chose to do!

The directors come ready to dismantle and deconstruct, but the show hampers them, initially, by being too floppy to use in battle: “1776” has a very silly first act, which alternates between bluff, talky exchanges and wacky songs, meant to keep us entertained. The act ends with a postcoital Martha Jefferson (Eryn LeCroy) singing, suggestively, “He Plays the Violin,” which is just not the sort of thing you can maintain a Brechtian attitude about—not even if you have Jen Schriever make the lighting very stark and Scott Pask make the faded-curtain set very glum. It should be a freewheeling scene, particularly since LeCroy has a huge voice, built for light opera, capable of stunning acrobatics. Paulus and Page cannot pivot from their insistent solemnity to address this type of goofiness, though, so they squash all the jokes. These first-act moments wind up being neither politically lacerating (it’s still a sex song about a violin!) nor fun.

The production gets onto firmer ground in the more substantial second half, and the musical reaches a peak with “Molasses to Rum,” a furious indictment of Northern hypocrisy sung stirringly by Sara Porkalob. Concealed beneath its frock coat, the latter part of the musical is very angry, and this is the fuse that catches light from the ensemble’s obvious sense of mission. Stone put a lot of good analysis into the book: that slavery was the rotten board that would sink the ship, that women had been forgotten because they weren’t in the chamber while Revolutionary soldiers could be forgotten even when they were. A courier from George Washington’s desperate front lines channels a dead boy: “Momma, hey, Momma, come lookin’ for me.” The anthem is performed by Salome B. Smith, who sings the walls down and, by the way, provides the production’s finest argument. Stern looks do not get us very far politically or artistically, but the show’s musical high points still have power: they get the signatures; they rally the troops; they ring the bell.