I haven't seen the London production, but the problem with doing this show in America is that you will compete with the film. No getting around it.
The answer for most productions (including the failed original in the '80s) is to throw a lot of money at it, and try to impress audiences with spectacle. That's why it rained on the stage.
I would think such a gamble on Broadway today would be a lose-lose scenario. If you don't give it a lavish production, you won't bring the people in, and if you do, you'll never recoup, due to the insane overhead it would take to give the audiences what they want.
Besides, "Singin' in the Rain" would never work as a "factory" production. And what I mean by that is a show with no stars or personalities. Something that is basically Disneyland on stage with interchangeable performing robots, that are highly capable but would never be all that distinguished from the next robot who replaced them.
Singin' in the Rain IS a personality show, and it would need strong leads and, dare I say it, STARS to play the four principal roles.
Ain't never gonna happen. Unless you get someone with an open wallet and a clueless head who doesn't care about recouping.
"Singin' in the Tax Write-Off!"
"Jaws is the Citizen Kane of movies."
blocked: logan2, Diamonds3, Hamilton22