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....