Newtonian Galilean science is what revealed to us that the world is not as it seems to common sense and everyday experience. Relativity and quantum theory do not tell us that the pictures of space and time and matter provided by Newton-Galileo are 'grossly misleading,' but that they are approximate and very adequate for many practical purposes. It is the 'common-sense' world picture that is misleading, not classical physics.
Rationality is concerned with reason, logical consistency, empirical proof, etc.
What is called 'the ontic realm' vaguely corresponds to this. However, unlike what is claimed for the ontic, our knowledge of the transrational can be very complete, indeed even more so than our knowledge of the rational aspects of the world, if only because it is based on intense personal experience. Yes, if we may start with this hypothesis, we may explore aspects of the 'larger set' through quantum physics, meditation, Buddhism, or whatever else. But if we start with the hypothesis that the 'the larger set' is merely a consequence of complex neural chemistry, neuroscientists may not be on the wrong track, after all. My own hunch is that quantum physics and neuroscience may some day merge exactly as quantum physics and cosmology have done.