I know you're looking for theatrical reference points but having worked on two prior productions of this show, my recommendation would recordings by Manhattan Transfer (the COA vocal arranger was and may still be their music director), Singers Unlimited and the like to give them the students the right "feel".
There are harmonically complex moments from some classic shows that approximate some of the easier pieces of COA ("Oldest Established" from G&D and some of the background vocals in "Sit Down You're Rockin' the Boat", "Standing on the Corner" from "The Most Happy Fella", the repeating "Thank You, Thank You" bit from "She Loves Me") but those shade towards a more barbershop/glee club idiom, where the chords, when sung properly, ring out and "sound right". In COA, there are many instances where even a given chord, sung 100% correctly, won't "sound" right (to most high school singers at least) without the chord before it and/or the chord after it and/or without the instrumental accompaniment.
Probably the hardest music I've ever had to teach in my life. And definitely the hardest parts tapes I've ever made in my life. Good luck.
"No matter how much you want the part, never let 'em see you sweat." -- Old Dry Idea commercial