What about "I Want to Be Bad" by DeSylva, Brown, and Henderson from "Follow Through"? It is definitely conducive to the nasaly accent, and to my knowledge is not overdone. It should fit your range, as I am a soprano and have sung it. It does have a few belty sections, but if you feel capable to sing Audrey I'm sure it's nothing you can't handle. It's an older song, so it won't reflect the 60's style of LSOH, but it is in the same vein as "Adelaide's Lament" in humor and range.
"I am concocting a seduction. I do not require a patissiere."-Boston Marriage