I'm focusing on the second question, which is related to setting and metaphysics more than it is on plot.
Allow me to quote from Tzvetan Todorov's The Fantastic in length, because it is useful in order to understand the dynamics involved.
In a world which is indeed our world, the one we know, a world without
devils, sylphides, or vampires, there occurs an event which cannot be
explained by the laws of the same familiar world. The person who
experiences the event must opt for one of two possible solutions:
either he is the victim of an illusion of the senses, of a product of
the imagination – and laws of the world then remain what they are; or
else the event has indeed taken place, it is an integral part of
reality – but then this reality is controlled by laws unknown to us …
The fantastic occupies the duration of this uncertainty. Once we
choose one answer or the other, we leave the fantastic for a
neighboring genre, the uncanny or the marvelous. (1973, 25)
What this means for your case, is that you need to understand the connection between genre and metaphysics involved.
- Case A: there are demons, and the whole reality as we know it has to change (we're scared because there are demons and reality as we know it doesn't exist).
- Case B: there are no demons, but we are losing our mind because we are seeing them in front of us (we're scared because we're going insane).
- Case C: we don't know what's going on; there might be demons, we might be going mad (we're scared because we don't know what's going on).
If you want your story to be unambiguously supernatural in terms of affective power, then the horror elements must be presented as such. You did mention Lovecraft, but bear in mind that madness and ambiguity is a central element in at least some of his work.
Although this is a plot matter in that sense, I think that your best option would be to prolong ontological ambiguity as much as possible, balancing between opting for the one or the other Todorovian branches (supernatural explained or supernatural accepted, to use a Gothic term).
In relation to setting in particular, and if you want to focus on how clinical and aseptic it is, you should precisely try to take life out of everything. That is, remove grit (metaphorically speaking, of course) from where it would've normally been.