dude this is great, and what a coincidence! We made a similar detective puzzle game a few months earlier based on GPT-4Turbo. We also encountered this problem of ai leaking key information too easily, our solution to that was A) we break down the whole story into several pieces, and each character knows only a piece, ai cannot leak pieces he doesn't know; B) we did some prompt switching, unless the player has gathered sufficient amount of information, the prompt would always provent the ai from confessing.
Give it a try if interested! also free to play! https://psigame.itch.io/netjazz2076