I believe that scientists and theologians both use their full range of psychological faculties all the time, unconstrained, in solving problems and the only difference between them is the kind of problems they're trying to solve.

The fact that scientists aren't using their full range of psychological faculties is precisely why they're different from theologians. Natural humans are creatures without logic. Reason requires an additional self-restraint that distinguishes between logic and illogic. If you want the full range, you'll have to deal with a thousand different fallacies that are part of the human birthright.