Little Me is a rare bird. I feel that the book is really a series of connected vaudeville-burlesque sketches with types rather than real characters. The show is meant to be performed and not acted.
If the director stresses this, the show will work.
The Music Fair tour in 1964 was full of performers: Jack Carter (from nightclubs), Kaye Stevens (a tall, busty, leggy nightclub comedienne-singer), (Ethel Merman's best friend) Benay Venuta and song-and-dance-man Harold Lang. It was also one funny show with plenty of good ad-libs by Carter and Stevens.
The one other show that fits this description of "meant to be performed, not acted" is Forum.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher