Do you have access to one of those compilation books? Or do you not want to choose one of those songs because it's "overdone"?
Also... which characters are you going for?
I like the idea of taking a song that shows off your voice and twisting it to fit the part you're auditioning for through your interpretation. Of course, that never worked for me and if you are auditioning in high school, I'm guessing your directors will be similarly unimaginative.
I mean, I like "Could I Leave You?" and "I Can Do Better Than That" but they're very adult songs. Just looking at that list (and not knowing either show well) Annie Get Your Gun, Paint Your Wagon, Sweet Charity, and South Pacific are decent places to look. Also, try The Apple Tree and A Chorus Line. Since it's Lippa, maybe take a look at Wild Party (also very adult) and see if you can make anything work in that. And don't be afraid to go with something like "Show Off" or "Shy" just because they're popular. If you can sing it well and perform it well, go for it.