I can't point you to much existing that isn't rights-based, at least around animal liberation, though John Zerzan (I know you were hoping to avoid A-P stuff) wrote something in the inaugural issue of Black Seed that I rather like. You might also want to check out
Personally, I can say that I appreciate the idea of animal liberation from a place more of affinity and solidarity. I don't like the ways in which I am confined and controlled and seen as a piece in a vast machine of industrial production, and I don't like to see other animals (whatever the species) treated that way either. In as much as I relate to and empathize with other humans who suffer at the hands of capitalism and civilization, so to other non-humans.
Combine that with my understanding of godlessness meaning that all of us evolved to what we are now not based on any divinely imparted hierarchy but rather to best survive given the circumstances, meaning people aren't superior to animals, we are just animals with a different skill set, and you pretty much have my take on it.
This is a somewhat longer thing I wrote some time ago about my perspective on animal liberation (and more specifically, being vegan) and how that has shifted from embracing the idea of animal rights to one wary of them, though I think I boiled down the most essential parts in the two paragraphs above:
I also particularly like this paragraph from the essay "The Harvest of Dead Elephants: The False Opposition of Animal Liberation":
"Animal liberation has the most potential as a direct act rather than an ideology. Liberations of animals violate their status as property. Sabotage and destruction of animal industries can be directed against the commodification of animals. However, when these actions are done with the ultimate goal of animal liberation, they remain confined to a perspective that cares only for animals. For example, many vivisection lab raid communiqués focus solely on the oppression of animals, usually in moralistic or ideological terms, while ignoring all the other exploitative and disgusting aspects of the university research lab or pharmaceutical company. Instead of breaking down boundaries to understanding social domination, actions like these erect them and promote limited perspectives that don’t take into account the underlying causes that turn animals into commodities. Likewise, the potential of these actions is stunted by their confinement to a single issue instead of being an act of solidarity linked to other social struggles. There are, however, some notable exceptions of people liberating animals and sabotaging animal exploitation operations without claiming their actions for animal liberation. These should not go without notice as they are positive because they do not demarcate themselves as relevant to only one aspect of domination but rather are attacks on one of many forms. If we see domination and exploitation everywhere, we must not limit ourselves; we must attack it everywhere it is found." (http://theanarchistlibrary.org/library/various-authors-a-murder-of-crows#toc53
In addition, if you haven't, you might want to check out the writings from Individualists Tending Toward the Wild in Mexico (http://theanarchistlibrary.org/authors/individualists-tending-toward-the-wild
). Not my very favorite stuff, but worth looking at, again, it has a pretty strong anti-civ perspective.