There’s been a lot of holiday parody under the bridge since the birth of American improvisational satire 57 or so Christmases ago in places like Chicago (the Compass Players, the Second City) and Minneapolis (Brave New Workshop). And by now, one might expect a show with a name like A Very Die Hard Christmas, Theatre Unleashed’s musical mashup of the John McTiernan terrorist-action movie franchise with countless Yuletide TV specials, to be a comedy slam dunk.

That it isn’t probably has less to do with the skills of its likable ensemble or director Gregory Crafts’ somewhat under-imagined staging, or even with the satiric acumen and fanboy erudition of Brave New Workshop alumnus Josh Carson’s text (the show is now in its fourth hit year in the Twin Cities).

Rather, opening a loony lampoon of a fictional Los Angeles terrorist assault the day after the real-life attack on San Bernardino’s Inland Regional Center (and less than a month after the bloody Paris massacre) may be the mother of all scheduling mishaps.

That said, Craft’s singular stroke of genius is the reverse-race casting of hero John McClane (a convincing Wade Wilson) and the airport limo driver Argyle (Adam Meredith, who also doubles as a terrorist). Liesl Jackson as wife Holly and Bradley Upton, who doubles as Alexander Godunov and as sidekick Sgt. Al Powell (here, the Burl Ives snowman puppet from 1964’s Rudolph the Red-Nosed Reindeer), both provide capable support. And David Foy Bauer does a creditable job hamming the Alan Rickman role as terror mastermind Hans Gruber.

Still, the show is hardly a threat to L.A.’s reigning kings of the musical-mashup parody, the Troubies, who could pluck this kind of low-hanging comedy fruit in their sleep — and do it without the disturbing stage spectacle of this production’s use of chillingly realistic prop assault rifles.

The Belfry Stage, Upstairs at the Crown, 11031 Camarillo St., North Hollywood; through December 19. (818) 849-4039,

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