Just what we need after the federal machine’s near-death experience last week: a documentary about Alexander Hamilton that turns out to be a compellingly loopy exercise in Founding Father vogue, fixating on the life and mind of the nation’s first Treasury secretary, who, among other things, devised a credit-based American economy that turned us into the most impressive army of borrowers and shopaholics the world has ever known.

Desperate to keep the viewer’s attention and set itself apart from 95 percent of PBS programming about the men whose faces grace our folding money, filmmaker Michael Pack and writer Richard Brookhiser’s “Rediscovering Alexander Hamilton” (airing Monday night on WETA) employs everything from clips of HBO’s “The Wire,” to tuneful meandering through the streets of Hamilton’s Caribbean boyhood, to the sight of engineers lifting his house and moving it a few New York City blocks to preserve history.

“Rediscovering Alexander Hamilton” is the documentary equivalent of the hybrid car: It has academic imprimatur in the expected forms of such well-known history writers as Sean Wilentz and Ron Chernow (it even drags out Gore Vidal once more), but it also has publisher Larry Flynt, Rupert Murdoch and Supreme Court Justice Antonin Scalia. And former Treasury secretary Henry Paulson. And, of course, columnist David Brooks.

But for every talking head it features, it also delightfully veers to the unexpected. The filmmakers sit down with women serving prison time in the Virgin Islands, whose circumstances are similar only in a symbolic way to the jail sentence of Hamilton’s mother in the 18th century. Yet, as Brook­hiser tells the women the story of one Rachel Faucett and the women think about it out loud, their experiences begin to remarkably resonate with hers.

On the island of Manhattan, Hamilton’s psychic home and final resting place, the filmmakers visit his alma mater, Columbia University (the former King’s College). Here, as if in some Jay Leno-style sketch, some of the students on the quad have never heard of him.

Then the filmmakers conscript hundreds of Virginia teenage boys to wear red or blue T-shirts and reenact (with inflatable swords) Hamilton’s lone military triumph, the 1781 Battle of Yorktown. And to illustrate the kind of post-Revolutionary War mon­etary disputes Hamilton took on as a New York lawyer, the filmmakers anachronistically reenact a case on the set of “The People’s Court” with deadpan seriousness and period costumes.

As with their “Rediscovering George Washington” in 2002, Pack and Brookhiser use this inventive style as a hedge against the utter boredom that might usually greet a two-hour documentary about the Federalist Papers. While it’s a refreshing departure, it can be a wee bit grating at times.

Brookhiser narrates and interviews his subjects with the certain false naivete of a humor columnist, not unlike the historical show-biz shtick used by contemporary writers such as Sarah Vowell or that popular professor on any campus who has found a way to keep undergraduates awake.

Despite such vibrant efforts, the film feels a half-hour too long. When, at last, it is time to revisit the unseemly subject of Hamilton’s death at age 47, after his infamous gun duel with Aaron Burr in 1804, Pack and Brookhiser assemble a panel of Baltimore gangbangers, who go by such street names as “Big,” “Donut” and “Steel,” to explore current ideas of when and when not to counter disrespect with gunfire.

“Burr believed that Hamilton had called him ‘despicable.’ Is that something that would make someone in Baltimore angry today?” Brookhiser asks with straight-faced curiosity.

“Someone sayin’ I’m ‘despicable,’ that’s not gonna faze me,” Donut replies. “That’s something Daffy Duck says, you know’m sayin’?”

Oh, he knows what you’re sayin’, Donut. You can almost sense Brookhiser masking his delight, as his varied subjects serve the film’s agenda: to bring Hamilton and his economic principles to life through a number of surprising, relevant and entertaining insights.

‘The Great Famine’

Returning to something much more recognizably PBS in shape and sensibility, the “American Experience” series has “The Great Famine” (also airing Monday night on WETA as well as on MPT), a grim but mesmerizing look at the nascent Soviet empire’s disastrous famine that began in 1921, brought on by drought and overzealous wealth redistribution.

Based on historian Bertrand M. Patenaude’s book “The Big Show in Bololand,” this documentary focuses on the American Relief Administration, a team of determinedly optimistic rescue workers led by Herbert Hoover.

“The Great Famine” is one of those documentaries that ben­efits from the distance of time and history, yet comes with a plenitude of archival film footage and photographs and, in a few cases, some first- and secondhand recollections.

Although history is not kind to Hoover’s presidential economic legacy, he was a keen bureaucrat when it came to responding to the Soviet disaster. The ARA had to battle anti-communist sentiments at home as well as logistical nightmares abroad, but it persevered, and life in the Soviet Union eventually improved.

In the way that leaders are sometimes able to weigh human life against politics, this fact would haunt Hoover (nickname: “the Great Humanitarian”), who worried later that even though he had saved the lives of millions, he had also rescued the Soviet regime from an early extinction.

Rediscovering Alexander Hamilton

(two hours) airs Monday at 10 p.m.

on WETA.

The Great Famine

(one hour) on “American Experience,” airs Monday at 9 p.m. on WETA and

at 10 p.m. on MPT.