I don’t think UChicago is the best fit for you.
Your academic / career interests are better served at Penn or Cal.
I can’t imagine arriving late to the game at UChicago and having to try to catch up with the Core … at a college that is really, really challenging. It’s just a bad idea. If you go to UChicago, you may end up having to spend an extra year / more $ in order to graduate.
If I were you, I would be deciding between Penn and Cal, and I would choose Penn, despite your reservations.