First of all, I love this class.
How is your opinion on letting Shillelagh be str/dex/cha based? State certification has nothing to do with the patron and is likely a homebrew background feature (from its name).
I would rather give it a feature that represents what you had to sacrifice to the Truth. Think a feature like
oracle curses. Basically a situational or minor+RP drawback for a single advantage (Izumi Curtis) or a major drawback (lost limb, blind) for two advantages (Mustang, Edward).
Example:
Internal organs: You lost the ability to conveive children. You have disadvantage on saves vs. poison. If you receive a constant advantage from any other source, these features cancel out.
Instead, once per short rest you get advantage on any strength check (be it attack roll, ability roll or strength save).