Nice - I do something similar in a semi manual way.
I do find Codex very good at reviewing work marked as completed by Claude, especially when I get Claude to write up its work with a why,where & how doc.
It’s very rare Claude has fully completed the task successfully and Codex doesn’t find issues.
Claude is also good at that. I made a habit of asking "are you sure?" after a complex task. It usually says it overlooked something.
I created the first version of loop after getting tired of doing this manually!