"But what BroJoeK seems to attribute to St. Thomas is the understanding that these categories are effectively mutually-exclusive, and one is better than the other in gaining "real-world" knowledge."
I think I've been very careful to point out in numerous posts that Aquinas himself did not consider the two realms in conflict with each other.
But neither did he deny the existence of two realms, which is what all your illustration seems determined -- come heck or high water -- to do.
And the whole point of this -- the reason I keep bringing it up -- is it shows precisely when and where natural-science and theology split apart as separate realms of knowledge, with different methods of thinking.
After Aquinas "natural-philosophy" (aka "science") becomes a separate realm from theology, then called "the queen of sciences".
Of course Aquinas would strongly oppose what we call "philosophical naturalism", but the methods of science as a discipline distinct from theology began with Aquinas.
At least, that's my understanding.
Again, must run...
Because you categorically separate them does not mean they are factually "separate" in Reality, let alone mutually opposed.
The scienific method is based on perception. But human reasoning is based on apperception; that is, movements of the mind that are not subject to direct perception. As an entity, the mind itself is not capable of being "perceived" as is the case with an object of sense perception. But we accept that the mind must exist because we "see" what it does.... All thinking takes place in this entity, which is perfectly undetectable by sense perception.