The actress/singer/comedienne who really would have been perfect for the part was the late and amazing Laurie Beechman.
The original "Star-to-Be" in Annie and the possessor of an astonishing trumpet-like voice, she went on to take over for Betty Buckley in Cats, and then took over as Fantine in Les Mis, when she was diagnosed with ovarian cancer, in 1988, at age 34.
She then proceeded to re-define what cabaret performance was, much as Streisand had done, at the Bon Soir in the 1960s.
Here is Laurie Beechman showing what her Fanny Brice would have been like, singing "The Music That Makes Me Dance" and recounting a conversation with Barbra about singing other people's songs:
LAURIE BEECHMAN SINGS "THE MUSIC THAT MAKES ME DANCE"
http://youtu.be/JWGd4AbQ65U We lost Laurie to ovarian cancer in 1998, at age 44. A memorial service was held at the Winter Garden Theater and the cabaret space at the West Bank Cafe was named for her.
But, oh, what a great Funny Girl she would have been!
"If you've been in extreme circumstances--
it doesn't have to be cancer,
it can be the death of a spouse, AIDS, anything--
and you've been lucky enough to survive,
it's incumbent on you to live the best possible life.
What's the point otherwise?" --Laurie Beechman, The Washington Post, 1996