My personal rule is never do anything by the composer when auditioning for a show. Not to say that you couldn't blow them away with something from L5Y, but if I were you, I'd look for something else. They will be hearing a LOT of JRB music, not only because it's for his show, but because he is the current "it man" among Broadway composers.
I'd steer towards something more unknown. The director obviously has a taste for lesser known composers / more "unconventional" modern theater songs - they are doing JRB after all. I'd look at some Adam Guettel (probably not Piazza, but there's good female songs in Myths and Hymns).
Also, I dunno how old you are, but there's an AMAZING song by Jeff Blumenkratz called "I Don't Mind." It's on Audra MacDonald's solo CD, and Victoria Clark sings it on his website (link below) - side note: I highly recommend you sign up for his podcast, it's brilliant. ANYWAYS, it's a great song, but is specifically for an older women. I'd check all the songs on the podcast though; Celia Keenan-Bolger sings one too that is equally amazing, but in a different way. And he has a songbook that I believe both are in.
Hope that helps! Good luck and keep us posted!
I Won't Mind