I know this is all just in good fun, but this thread does have me seriously thinking about it:
The problem with a Barb & Star stage musical is that it's almost...too intuitive? I think that sometimes movies come out that just scream "musical theatre!" but then they lose their charm when they actually are adapted. The campy, theatrical elements of Barb & Star mostly work because they're on film - a medium that usually bends toward realism. That contrast allows the ridiculous comedy to land more easily (this is why, IMO, the Mamma Mia movie is worlds better than the stage show). If Barb & Star were transplanted to the stage as-is, it would probably just read like a run-of-the-mill, substance-less musical comedy - and the humor would almost certainly feel like a flat mockery of the film.
In order to make it work, they'd have to dial-up the camp factor several notches, and you'd need the best comedic actors/creatives in the business to pull it off. I'm not saying it can't be done, but you'd have to be very careful about who you hire, and how they approach it. And they would really have to make it their own.
IMO, Shaiman and Whitman are not up to the task at all. They're way too bland. They would just write a bunch of basic, upbeat songs that have a lot of energy, but no character. I'd love to see Rachel Bloom do it - she can even write the book too. As for the director, I would go with Margot Bordelon - she has yet to work on Broadway, but she's very well-established Off-Broadway. And this kind of project is right up her alley: she's incredibly skilled at capturing very specific, slightly weird, silly-but-smart comedic tones.