(Still feeling out possible answers.)
Thesis: Metaphysics is methodologically supernaturalist. This can be seen by comparing it to the inquiry into heat, which is methodologically naturalist.
A discourse into heat presupposes that there is something that heat is per se and convertibility. St. Thomas thought this was fire (and so he thought everything that was hot had the element of fire mixed in: blood, warm stones, hot tea, etc.) Fire was not just hot of itself, it was what heat was. The theory was wrong- the consensus seems to be now that heat energy is the quivering of a sufficient number of molecules. All that we’re interested in here is that “the quivering of a sufficient number of molecules” plays exactly the same role in an explanation of heat that fire once played, and the search for such a thing is exactly what the inquiry into heat is looking for. Aristotle called this what was hot kath’ auto and kathalou, and the Scholastic tradition calls this same thing per se and primo.
Though we can’t know before the inquiry whether the per se and primo of heat is fire or quivering, we can see some outlines of the answer in advance: for example, the per se and primo of heat must be something physical and contingent. And so there is a methodological naturalism with respect to heat and other things like it.
But the case is different in the inquiry into existence. The per se and primo of existence is that which exists by its very nature or essence, and in this sense it is utterly divided from a methodologically naturalist sort of discourse. The inquiry into existence is, in fact, methodologically supernaturalist, because we can discern in the very outlines of possible answers that we are looking for an essence whose nature is to exist.