Idina is very talented, but her age and her voice aren't right for this role. 15 years ago, sure. I'd rather see her in a revival of "Gypsy," where I think she has the allure and spirit for Rose. Honestly, it would be just as big as her doing "Funny Girl," and a better fit. (Realistically, she's one of four Broadway names who would do the next production. Her, Donna, Audra, or Sutton.)
Lots of great ideas in this thread: Shoshana Bean, Lindsay Mendez, Jessie Mueller. I'll also throw in Annaleigh Ashford and Christina Bianco to the mix. Ariel Sta'chel or Santino Fontana as Arnstein. Unless you get someone like Gaga, I think you'd need to set this up at a nonprofit or really stack the cast with Broadway names. The recent revivals of "Fiddler" and "Carousel" weren't huge financial wins.
"I saw Pavarotti play Rodolfo on stage and with his girth I thought he was about to eat the whole table at the Cafe Momus." - Dollypop