Actually this might work if the actress playing Mimi comes across older. The main relationships (yes, I know, it is about the relationships of all of them), in my opinion, are the Mark/Roger and Roger/Mimi relationships. If Mimi plays older, I think this will work.
And, Mark and Adam do play younger than their actual ages. He looks older in the movie because of the hair. Keep the hair short, there shouldn't be a problem, especially on stage where distance will be their friend.
The truly beautiful should be lawfully restricted from wearing clothing; and the truly butt-ugly should be lawfully mandated from going naked.