"I love to create from scratch, so when I can, I do," Brightman says. "I'm not a good impersonator, so I'm not worried that I'll be too good at being the guy that can mimic."
Beetlejuice has just begun a world-premiere five-week run at the National Theatre in Washington, DC, and the show is slated for a March opening on Broadway.
While the title character famously has just 17 minutes of screen time in Tim Burton's twisted fantasy-comedy, which focuses on a recently deceased couple who ask the demon for help haunting their former home, Brightman's Beetlejuice - or Betelgeuse, as the character's name is alternately spelled - is the driving force of the musical.
In a revamped narrative, this Beetlejuice focuses on the relationship between the meddlesome, manic fiend and Lydia, the goth teenager whose family moves into the haunted house.
The character of Beetlejuice walks a tightrope as a villain the audience can't help but find endearing in his quest to wreak havoc on the mortal world. Brightman's obvious amiability is embedded in the role.
"He's always got a really good attitude," Beetlejuice director Alex Timbers says of his star. "When everyone is exhausted, he's the first one leaping up onstage to get something done. I find him very inspiring, and I think the company does, too."
Brightman, who didn't meet Black until School of Rock had been on Broadway for months, hasn't spoken to Keaton about his new part.
"I'm not good at reaching out, mainly because of my past of reaching out to girls I thought liked me and getting shot down every time."
But Brightman thinks Keaton would appreciate his take, which has been coloured by moments he improvised throughout various readings, workshops and rehearsals over the past two years.
"It's very different, extremely different than Michael Keaton," Brightman says. "It could be like Beetlejuice's younger brother. There's still a voice, there's still a thing, but it is actively not the one in the movie."
Brightman's creative instincts have extended from the stage to the page. He is co-writing musical adaptations of the 2010 film It's Kind of a Funny Story and the 1986 children's novel The Whipping Boy.
Reflecting on how the Beetlejuice team shaped the character around Brightman, Timbers says: "For somebody like Alex to be such a funny writer, it helps so much. He gets what the authors are going for, he's able to collaborate with them, with me, with such sophistication of understanding all angles of the craft."
Brightman has stretched his ambition to television too, selling a family sitcom to NBC last fall. The show didn't get made, but Brightman was undeterred: He's now sitting on four "fully fleshed out" pitches for comedy series, plus an idea for a horror anthology in which each episode focuses on a common recurring nightmare.
"I have the type of anxiety that wakes you up and says you're not doing enough, even when I'm in a show like this.
"Anxiety is a serious condition that I have my ups and downs with, but anxiety and depression have led me to finding ways to combat it - and what combats it is work."
After seeing the way School of Rock opened doors for him, Brightman hopes Beetlejuice can be the springboard that gets some of his projects off the ground. If that means being seen by some as "the guy that does all of the movie roles", that's fine by him.
"When I started in New York 15 years ago, it was like, 'I don't care if they like me or not - I just want them to notice me'.
"If you just keep your head down and work, you will have zero time to go, 'Is what I'm doing worth it?' And you'll just have a product at the end of it. Good or bad, you'll have done something. That's been my whole career."
