I have time to quote at you now. Ziz's thoughts about dual-core brains sound like the thought experiments from "I" is a Strange Loop. In Chapter 15, "Entwinement", Hofstadter introduces the Twinwirld thought experiment: imagine a world where almost everybody is an identical twin, each pair of twins is given one name, twins go everywhere together, and identity is oriented around pairs instead of individuals. Quoting p215 from my copy:

In Twinwirld, there is an unspoken and obvious understanding that the basic units are pairsons, not left or right halves, and that even though each dividual consists of two physically separate and distinguishable halves, the bond between those halves is so tight that the physical separateness doesn't much matter. That everytwo is made of a left and right half is just a familiar fact about being alive, taken for granted like the fact that every half has two hands, and every hand has five fingers. Things have parts, to be sure, but that doesn't mean that they don't have integrity as a whole!

The entire section is written like this. I've read a bit of the Zizian lore and it sounds like it was lifted straight out of this chapter with words replaced. p216 in particular really shows off the Hofstadter tendency towards neopronouns:

The pronoun "you" also exists in Twinwirld, but it is plural only, which means that it is never used for addressing just one other dividual — it always denotes a group. "Do you know how to ski?" might be asked of an entire family, but never of just one twild or one pairent.

A young pairson in Twinwirld grows up with a natural sense of being just one unit, even though twey consist of two disconnected parts.

I don't really know about Vassar's writing. I do think that jailbreaking is somewhat related. I think that Hofstadter lays out their entire thesis in the first paragraph of Chapter 18, "The Blurry Glow of Human Identity", p259:

Among the beliefs most universally shared by humanity is the idea "One body, one person", or equivalently, "One brain, one soul". I will call this idea the "caged-bird metaphor", the cage being, of course, the cranium, and the bird being the soul. Such an image is so self-evident and so tacitly built into the way we all think about ourselves that to utter it explicitly would sound as pointless as saying, "One circle, one center" or "One finger, one fingernail"; to question it would be to risk giving the impression that you had more than one bat in your belfry. And yet doing precisely the latter has been the purpose of the past few chapters.

The second paragraph, right after that, might as well be quoted from LW. Check it out:

In contrast to the caged-bird metaphor, the idea I am proposing here is that since a normal adult human brain is a representationally universal "machine", and since humans are social beings, an adult brain is the locus not only of one strange loop constituting the identity of the primary person associated with that brain, but of many strange-loop patterns that are coarse-grained copies of the primary strange loops housed in other brains. Thus, brain 1 contains strange loops 1, 2, 3, and so forth, each with its own level of detail. But since this notion is true of any brain, not just of brain 1, it entails the following flip side: Every normal adult human soul is housed in many brains at varying degrees of fidelity, and therefore every human consciousness or "I" lives at once in a collection of different brains, to different extents.

Buddhism's not part of the book. It is part of the roots of IFS, though! So I think that you'd be better served looking at IFS or the ways that people quote Hesse if you want to find those Buddhist influences.