Let’s do the Time Warp again — this time, on the small screen.

Fox is following up on the success of Grease Live! by reaching back into the 1970s to remake another beloved musical: The Rocky Horror Picture Show, the raunchy 1975 cult classic that still manages to shock and titillate after all these years. (Can you believe audiences were singing along with a “sweet transvestite from Transsexual, Transylvania” four decades ago?)

And the show is getting a timely update, with transgender actress Laverne Cox (Orange Is the New Black) starring as the lascivious Dr. Frank-N-Furter. (Don’t worry: The original Frank-N-Furter, Tim Curry, is back as well, as the Narrator.) The new cast boasts music-industry cred (Adam Lambert as Eddie, Christina Milian as Magenta) and tween-TV star power (Victoria Justice and Ryan McCartan as Janet and Brad), and with High School Musical’s Kenny Ortega on board as director and choreographer, you can expect more than a few toe-tapping musical numbers.

The cast and crew behind the new Rocky Horror — debuting Oct. 20, just in time for Halloween — brought the party to San Diego Comic-Con on Thursday night, screening the first 25 minutes to a rowdy crowd of Rocky devotees (no, the production won’t air live; it was filmed in advance) and discussing the challenges of adapting one of the weirdest musicals out there.

Executive producer Lou Adler worked on the original film, and when he saw the crowd’s enthusiastic reaction to the new footage, he told the packed ballroom, “I think our biggest fear just went away.” He emphasized that the whole production was determined to “never lose the fact that the fans have carried this film for 40 years.”

There are a few noticeable tweaks to the Rocky Horror we know and love: A girl in front of a movie theater sings “Science Fiction Double Feature” rather than just a pair of lips. Frank-N-Furter enters on a giant crane rather than in an elevator. And Brad and his pal exchange a fist bump (!) at the opening-scene wedding. Plus, echoing Adler’s point about the fans, they even incorporate a movie-theater audience to replicate the call-and-response fun from the film’s famed midnight screenings.

But for the most part, this Rocky Horror sticks to the script: We get an appropriately chirpy rendition of “Dammit Janet,” an grandiose take on “There’s a Light” — during which the Comic-Con crowd dutifully lifted their illuminated phones into the air in tribute — an epic “Time Warp” (Penny Dreadful’s Reeve Carney is an early highlight as Riff Raff), and Cox’s grand entrance in glittery red lingerie with “Sweet Transvestite.” This is clearly a Rocky Horror made by fans, and made for fans.

Of course, there was some concern that the new take wouldn’t live up to the original. Ortega says they consulted the president of the Rocky Horror fan club; he even has a cameo in the film as the wedding photographer. Curry is obviously the link bridging the two versions; the Comic-Con fans cheered the loudest for his name in the credits. And Curry was happy to participate. In fact, he actually called up and requested to be a part of this production, Ortega revealed. Adler says Curry has already seen the new version and given it his blessing: “He said, ‘You betcha.’ He liked everything about it.”

Most of the cast wasn’t born when the original Rocky Horror hit theaters, but they all remember the first time they saw it. Justice says she first watched it in fifth grade, and then later went to a midnight screening in her teens with some famous pals (including Hunger Games star Josh Hutcherson) “... and our moms.” McCartan first saw the stage version, and he had an awkward family connection, too: “My sister was in it… and I saw it with my mom.”

Given the sexually graphic nature of the material, it did put the cast members in a few… uncomfortable positions. Milian remembers that during rehearsals, “we all had to look each other in the eye and circle each other in… what can I call this? It wasn’t an orgy.” (Adler helpfully adds, “You were in the soup together.”) After a decade starring on squeaky-clean kids’ shows like Zoey 101 and Victorious, Justice laughs, “I think I can say with certainty after doing this that the Nickelodeon chapter of my life has closed.”

Watch the new "Time Warp"-themed trailer, below.