I was once in a similar position, and I did THE PAJAME GAME. In addition to Babe, Gladys, Mabel, and Mae (who gets to shine in the "Her Is" reprise), I took a group of about 8 girls to be "Babe's Girls," and they were the group who did "I'm Not at All in Love," "Think of the Time I Save," and danced the tango in "Hernando's Hideaway."
You can recruit a non-singing boy to be the boss character.
It was a tremendously fun show, and the audience loved it. My Hines was a naturally comedic kid, and he brought the house down with the pants falling/tripping routine, so much so the principal acknowledged it over the PA on Monday morning. He could sing, but I also had to recruit him. In the movie he's a cantankerous old man, but don't go that route.
Don't cut the ballet! Besides the fact that you really need it, you can have lots and lots of fun with it. Basically you need a ballet dancer for Gladys, but the other two parts can motion their way through. The ballet isn't in the movie, but it goes like this . . . Hines leaves for work, and while he's gone, he imagines that Gladys is cheating on him. He dresses up as various people (a muscleman comes to mind) and Gladys flirts with him, but then Mabel comes in with angel's wings and reprimands him. It's very, very funny, and my audience loved it.
I did a Dream Gladys casting because my ballet dancer wasn't an actress really. I had Gladys walk out the door waving to Hines, and then return with a newspaper. The returning person was my Dream Gladys in the same costume. It worked really well.
I did cut the short bit where Babe undresses in the kitchen and finished in her slip. Forgive me, MTI, but I couldn't find my way around it.
So . . . That's something to consider. Oh! I made Sid's helper Charlie into Charlee--a girl with a bandana on her head (short for Charlene). We do what we must . . .
Braodway Blog: Only One Night Only (the Tonys post)