I don't have a handy new name for my philosophical worldview. I just try to combine all the things that strike me as true, so by now it's gotten pretty complex. It's naturalistic, pantheistic, cosmicist, existential, old atheistic philosophy. It's similar to Kronman's approach in Confessions of a Born-Again Pagan, in that we're both taking up the Nietzschean problem of looking for a viable religion in the face of the modern collapse of meaning. But my criticisms of Christianity are different and more extensive.
I'd say cosmicism, Buddhist nihilism, or a belittling transhuman perspective would be close to the unvarnished truth in Thomas Nagel's sense. These forms of detachment amount to the "view from nowhere" which is objectivity. Philosophical or mystical objectivity, as opposed to scientific instrumentalism, is inherently dehumanizing.
When you speak of "levels" above nature, you're already naturalizing or humanizing them.
I think of meanings, purposes, and the like as artworks (abstracta, brainchildren). We assign meanings by imagining certain subjective relationships, as in animism or philosophy. When we objectify and detach from all our personal preoccupations, nature becomes a ghostly museum of living-dead artworks or mindless creations. The natural order is full of (mostly negative) aesthetic value because the universe created itself (as in pantheism), but these aesthetic meanings are strange and alienating to social beings like us because they're mindless (contra theism).
Human meanings and the existential revolt are oppositions to the horrors of the wilderness. Nature has its meanings and evolutionary purposes, and we have our intelligently designed, artificial ones. It's a battle between mindless and mindful arts.