You are completely correct: this is a zombie game with a thin coat painting. As much as I enjoyed working on it, this is my main grievance with the final product.
While the mechanics don't explicitly encourage you to act on the Uma's idol side, you can definitely have an Uma sing to cheer up a comrade, deny reality and dance to her death as she snaps, or make a last stand on stage to attract all zombies and help her friends escape. Depending on the tone of the game you end up running, it can be grotesquely comical or played straight for horror. There are no rules for it. But I could've informed it in my lore blurbs.
I'm relieved to hear that Prez made a good impression. While fighting her with classic survival horror weaponry isn't super on brand, don't forget about all the improvised weapons you can loot on the school grounds!
Thank you so much for your feedback!