Regarding your point about cosmologists who aren't bothered by nature's alienness, I'd take that to indicate scientism. Modeling nature is a scientific act. Understanding its implications for a noble worldview is a philosophical or religious one. Just because scientists may not engage in philosophical interpretation, doesn't mean the interpretation is illegitimate (unless the scientist contradicts himself by assuming philosophical scientism).
This article was inspired, as I recall, from your suggestion that I should develop an ontology.
I think it's not a matter of definition, but of stretching intuitions. Understanding nature's wild aspect, without resorting to animistic analogies (such as comparisons with wild animals), isn't so easy, so I don't claim to have fully explained the nature of cosmic wildness. It's like asking what exactly Schopenhauer should have meant by nature's "will."
I interdefine "cosmic wildness" with "monstrous," but the problem returns: Is there a non-animistic sense of "monstrous," one that isn't wholly arbitrary or negative (monstrous = other than us)?
Cosmic wildness and consciousness seem to me equally mysterious.
I take up this question in several articles, including an upcoming one about the nature of accidents. Check out the last article listed below, on mathematics.