@Thomas,
How can you doubt that after saying that "it (consciousness) navigates an abstract, data-compressed geometry generated by our brains' image-processing"?
If you flood that cave with the right frequencies of sound, bats will be blind in there, while humans won't notice anything.
If the cave had something in it that jammed the bat's sound signals, it would just be a black hole of nothing to the bat, while humans would still see it as a cave.
So while the "geometry of the cave is the same", as you put it, what we can detect of it differs between species with different means of detection.
My argument is that it is more accurate to refer to reality as the species-specific existence we experience. The "common geometry" is part of this experience, but if we state that
it is reality, we are ignoring the possibility that
it is only
potential reality, becoming actual reality only within the context of a species-specific experience.
This idea or proposition is a shift in perspective from a materialistic one which puts the existence of a mind-independent reality as a fundamental axiom, to a perspective that starts with the realization that, as you put it, consciousness navigates an abstract, data-compressed geometry generated by our brains' image-processing.