Well, for me, that transcendent something has to do with the cosmicist side of naturalism. What transcends our comprehension or at least our intuitions is the whole universe, the alien scale of nature, or the absurdity of its self-creativity. We evolved to intuit only terrestrial problems, but the universe contains trillions of other planets. How much more transcendence do we need than that? The talk of supernature is superfluous. In fact, the heavens used to be identified with outer space.

Also, I say somewhere in the article that "spiritual" has connotations that atheists will want to reject, so the word isn't as important as the concept. I'd rather speak of existential depth of character than spirituality.