I tried to write a different "convince an AI" game about a year ago, but it was hard to work with, hard to figure out a business-model for, and more importantly-- it just wasn't very fun to play. Maybe there's a different scenario than the one I chose.
I tried prototyping a detective game also but like you said it ends up being a wrapper for a LLM and it’s a bit chaotic, not much more fun than just talking to the LLM in a web interface or whatever