A quixotic hunger for completism, for making a mountain out of a mountain, rests uneasily at the core of “The Wooster Group’s Hamlet.” The indispensable avant-garde company has chosen to apply its potent blend of virtuosic performance style and high-tech visual trickery to a deserving pinnacle: “Hamlet,” the iconic Shakespeare text that Harold Bloom has christened a “poem unlimited.” (Unlike commencement speakers everywhere, Mr. Bloom can get away with quoting the congenital blowhard Polonius like that.)

In this production, the Wooster Group director, Elizabeth LeCompte, sets out to approximate, more or less in its entirety, a modern-dress 1964 Broadway production that was directed by John Gielgud and that starred Richard Burton. Snippets of other “Hamlet” films surface here and there, but Ms. LeCompte and her cast, led by the arresting Scott Shepherd in the title role, do their levelheaded best — or whatever passes for levelheaded in Wooster’s fractured world — to re-create the Burton mounting, which was filmed for a “Theatrofilm” airing in movie theaters nationwide.

That film literally looms over every second of the Wooster Group’s technically impressive, if ultimately questionable, efforts: An enormous video screen takes up much of the upstage wall, screening nearly all of the film. (Mr. Shepherd periodically calls for a bit of fast-forwarding.) But merely lip-syncing a decades-old “Hamlet” wouldn’t be nearly daring enough for this intrepid troupe. And so Ms. LeCompte and her reliably top-notch design crew have subjected the Burton “Hamlet” to the usual Wooster dislocations and disruptions; just as cell replication inevitably leads to DNA errors, this voyage backward has resulted in lost frames and milliseconds throughout.

The on-screen characters lurch forward or backward, arms jutting out and almost immediately sliding back into repose. And, of course, Mr. Shepherd, Kate Valk, and the rest of the crew follow suit, hitching and jerking their way through the play. All the while, a coterie of stagehands, sometimes including Mr. Shepherd, rotates the Spartan props accordingly, synchronizing their movements with both the film’s various camera angles and with its temporal hiccups. Equally intriguing are the ghostlike comings and goings of Burton, Hume Cronyn, Alfred Drake, and the other 1964 actors, who have been stripped in and out of the on-screen action through a distinctly Woosterian brand of digital trickery. (Six men and women are billed in the program as “video erasers.”) As their too-solid flesh melts, the ephemeral nature of live performance serves as both a warning and a goad to their modern-day collaborators.

Still, if this be method, with apologies to Polonius, yet there is madness in it. (Now they’ve got me quoting the insufferable old coot, too. Incidentally, Bill Raymond does a fine job as the Wooster’s approximation of Cronyn, who was the first actor to win a Tony Award for a Shakespearean role.) The tantalizing “what next?!” rush of past Wooster Group ventures — which have subjected everyone from Chekhov to Gertrude Stein to beguiling upheavals — gradually dissipates as Shakespeare’s tragedy lopes into its final act; not even the company’s unimpeachable technological and mimetic skills can mask the fact that the company is yoked to Gielgud’s self-conscious, no-frills concept until the final credits roll. (Yes, the final credits roll on that giant screen.)

The core company does what it can to carve out its own vision of “Hamlet.” Mr. Shepherd, with his alert eyes and frazzled red hair, has none of Burton’s fleshy voluptuousness; instead, he gives his Hamlet a more laconic, vaguely Southern intonation, locating a tone that coexists peacefully between Burton’s plummy physicality and Mr. Shepherd’s own, more relaxed affect. This comfort may stem from the removal of the anxiety that inevitably accompanies finding a new take on these legendary soliloquies and quips. Is Hamlet really mad? What’s up with him and his mother? These standard — and by now somewhat tedious — questions have been replaced with a simple “What would — or, rather, what did — Burton do?” That Mr. Shepherd refuses to confine his exploration to this question is admirable; that he has been put into this position at all is puzzling and almost necessarily self-defeating.

Even with the peerless Ms. Valk essaying Gertrude and Ophelia and the Player King, each role with more stylistic precision and sheer love of craft than the next, “The Wooster Group’s Hamlet” features an augmented cast by the troupe’s standards. And not all the new additions have mastered the veterans’ blend of mimicry and innovation: As Laertes and a handful of other characters, Casey Spooner (of the electropop band Fischer spooner) never quite clicks into the company’s earnest yet ironic vibe.

For a supreme example of this hard-to-define quality, watch the uncanny Ari Fliakos as he simultaneously apes and reimagines the monologue in which Claudius, Hamlet’s villainous uncle, displays a halfhearted remorse for his fratricidal acts. Keeping pace with the manipulated source material is tricky enough; embodying the role with legitimate pathos and confusion while matching the digital hiccups is an altogether different accomplishment. Mr. Fliakos performed a similar feat in the Wooster Group’s “Poor Theater,” in which he performed a harrowing sequence by the legendary avant-gardist Jerzy Grotowski in unison with a Polish-language recording. Here, with the original material jockeying for the audience’s attention, both in its memory and on an enormous video screen, he transcends that previous experiment and creates a feat of alchemic wonder.

Until December 2 (425 Lafayette St., between East 4th Street and Astor Place, 212-967-7555).