It seems we mostly agree about the usefulness and applicability of gut feelings, as well as their limitations. (Of course, if someone else is aware of any research about their accuracy, I am still interested in seeing it.)

One way I would summarize the ideal setup is: during "downtime", use logic-based reasoning to come up with a rigorous and easy-to-apply procedure; during "crunch time", use intuition to generate probable avenues of investigation and likely candidates for diagnosis and solution; supplement with the pre-developed procedure to guard against biases and ensure correct usage of intuition-derived data.

Does this sound like a fair summary?