I think you're overcomplicating things a bit. Music can easily be divided into three broad categories—emotional, kinetic, spiritual. For composers in the first category music is primarily about expressing and exploring emotional states. It has found its greatest success, in the present day, in film music, but also retains a foothold in classical music (figures such as Austenite and Lowell Liebermann), metal and some forms of country. For composers in the second category—the oldest of the three, by far—music is intimately connected to the dance. Currently this genre is dominated by rock, pop, hip-hop and similar phenomena, though some classical music belongs here as well (Glass, Max Richter, John Adams). For composers in the third category music is an expression of the ineffable, an object of worship—thus spiritual music is not religious, as it would displace the deity in question. This genre is most successful in classical music where the reverential atmosphere can be enforced by concert hall traditions.
Classical music—most of which is spiritual in nature—can thus in turn be divided into four categories, with some overlap with other forms of music: I think of these as constructivism, deconstructivism, non- or anticonstructivism and reconstructivism. Constructivists are trying to build something new, in the Marxist sort of way; something that synthesizes its antecedents to build something greater. These are composers like Brian Ferneyhough and Francis Dhomont and Masami Akita. Deconstructivists take a more conservationist approach, recycling material in order to change existing traditions rather than turn them into new ones; think of Gabriel Prokofiev or Peter Ablinger or Laurence Crane. Anticonstructivists don't believe newness is desirable or even possible; pessimistically, the language of music has been exhausted, or optimistically, a sublime experience must be presented in a familiar way. Bent Sørensen, Valentin Silvestrov, Georg Friedrich Haas might all be examples. Reconstructivists' approach is ultimately about the extinguishment of the self. An ascetic approach to musical spirituality, they typically devote themselves to a single composer or style of the past; there are few of these, but they have found some success—see Brian Newbould's compositions in the style of Schubert, or Deryck Cooke's symphony in the style of Mahler. The severe restrictions of the reconstructivist approach mean it will never be as widespread as the others, but it has nevertheless had a degree of influence, particularly on the HIP movement (historically informed performance practice).