◇ Could this help me?
Yes for the pattern, with a verifiable condition as the requirement rather than a suggestion. Defining done and letting the agent work toward it is better than turn-by-turn supervision for anything with a clear finish line, and the design detail that a separate model evaluates the condition is the right one, since the model doing the work is the least reliable judge of whether it is complete. The failure mode to guard against is a condition that cannot be objectively checked, because an unattended loop with a vague goal will eventually declare success on work that merely resembles success. General practice, with two conditions: the completion condition must be objectively verifiable, and the loop needs a bound, since every unproductive turn costs the same as a productive one.
I want to give you a completion condition rather than supervising each turn, and I want the condition to be one that cannot be faked. Here is what I want done, described below. First, turn it into a condition that is objectively verifiable, such as specific tests passing or output matching a defined shape, and tell me plainly if any part of what I asked for cannot be expressed that way. Then propose a limit: how many attempts or how long before you stop and come back to me rather than continuing. While you work, keep a short log of what you tried and what failed, so that if the condition is never met I can see why rather than only that it did not finish.