I quite like this formulation, and if I had thought of it at survey time I might well have answered 'atheist(spiritual)' instead of 'atheist(nonspiritual)'.

Regarding emotional benefits: I sing in moderately serious classical choirs, where inevitably much of the music is set to religious texts. I get some but not all of the emotional benefits from this that I used to get from religious worship, back when I was a committed theist. I think I would get more benefits if the texts were not religious, and still more if the texts were humanist / rationalist / expressed beliefs that I actively profess.