Lee Ferris as Carl Perkins, Chuck Zayas as Jay Perkins and Billy Shaffer as Fluke in the National Tour of “Million Dollar Quartet.” (Jeremy Daniel)

Just watch him go, man.

That’s all you can think, beholding the crazy-good vision of Elvis Presley currently gyrating around the Kennedy Center’s Eisenhower Theater stage. Cody Slaughter is a liquid Elvis, hips twisting and lip curling to perfection in “Million Dollar Quartet,” an enjoyably freewheeling re-creation of the impromptu 1956 jam session featuring Elvis, Carl Perkins, Johnny Cash and Jerry Lee Lewis.

Slaughter’s singing? Well, that’s all right, too, as he more or less nails the King’s tenor quavers and baritone growls. Yet David Elkins’s taciturn Johnny Cash may be even more on the money. There’s gold in the deep, dark notes he mines for the grim classic “I Walk the Line” and other Cash standards.

Then there’s Martin Kaye as the punkish but prodigiously talented Jerry Lee, legs and arms moving like a pack of pistons at the piano. And Robert Britton Lyons puts a fine mean streak into his portrayal of Perkins, whether he’s hammering his rockabilly guitar with a nice dirty crunch or lighting into Elvis for stepping on Perkins’s hit “Blue Suede Shoes.”

If that makes this touring company of the recent Broadway hit sound like the theatrical equivalent of a wax museum, it shouldn’t. The copies are anything but lifeless, and anyway the show hardly pretends to be a picture-perfect rendition of what happened at Sun Studio more than 50 years ago.

Derek Keeling as Johnny Cash in the National Tour of “Million Dollar Quartet.” (Jeremy Daniel)

The souped-up drama doesn’t matter, but for the record, it asks whether Sun Studio founder Sam Phillips, played with appealing Southern ease by Vince Nappo, is losing all this groundbreaking young rock-and-roll talent he’s discovered. (Elvis had already left Phillips’s Memphis building.) Everyone’s contracts are somehow on the line at the same time, meaning there’s a soapy smorgasbord of secrets and gossip to chew on between performances of famous songs that almost certainly weren’t actually played that day.

You can’t even begin to make sense of why Elvis’s tag-along girlfriend (Dyanne, she’s called) commands the spotlight for the sultry “Fever” and the rave-up “I Hear You Knocking.” Nothing against Kelly Lamont, of course, who purrs and belts her heart out in the silly role. Nice work if you can get it.

Again, no matter. Director Eric Schaeffer, who for years has made quality sound a cornerstone of his musical productions at Arlington’s Signature Theatre, keeps things lean and sharp, and the show begins with a drawling voice-over declaration that “There ain’t no fakin’. These boys are really playin’.” That’s what makes “Million Dollar Quartet” a cut above most of the canned goods in the jukebox musical aisle; when the guys unplug and harmonize on “Down by the Riverside,” it’s dead-on 1956. The same goes when a bashful Elvis, goaded by Phillips to loosen up, becomes the Elvis of lore right before our eyes during “That’s All Right.”

Elsewhere the ramshackle quality of the original session gives way to polished rockabilly arrangements, as during a gritty workingman’s mash-up of “Sixteen Tons,” anchored by Elkins’s stately Cash, and “My Babe,” driven by Lyons’s aggressive Perkins. Either way, the straight-up takes on “Hound Dog,” “Great Balls of Fire” and the rest of the expected hits are all fresh and bracingly alive. Music director Chuck Mead conscientiously grounds the actor-musicians in the period, but whether it’s Kaye galloping at the piano and hitting keys with his foot or Elkins and Slaughter strumming and crooning, the players make it their own.

Take note: Slaughter leaves the show Sunday, which means Maryland’s own Billy Woodward will be Elvis for the remaining two weeks. Slaughter may be a tough act to follow, but the show was a hit for years before he arrived. “Gimme sumpin’ the hot-rodders wanna hear,” Phillips commands at one point, and that’s how it works. They rev it up and go.

Million Dollar Quartet

book by Colin Escott and Floyd Mutrux; original concept and direction by Mutrux. Directed by Eric Schaeffer. Musical arrangements and supervision by Chuck Mead; sets by Derek McLane; costumes by Jane Greenwood; lighting by Howell Binkley; sound by Kai Harada. With Corey Kaiser and Billy Shaffer. About 1 hour 45 minutes. Through Jan. 6 at the Kennedy Center Eisenhower Theatre. Call 202-467-4600 or visit kennedy-center.org.