Well, is your body either a single material entity, or a collection of members? No. It is neither, both, more than either. The cellular structure is present, so it is not a single object, but at the same time it is a contiguous collection of cells, so it is a single object. The limbs exist, and may map out the body, but is more than a collection of them. (It is the whole constructed of the parts of a human, to paraphrase Quine.) Beyond that, the matrix of cells, or the collected members would be a corpse, not a body. And, animated, it is a body, a thing with specific functions, and would be so even if you replaced the cells and members with functional equivalents.
By analogy to this (perhaps overly pedantic) observation, to me there are two logical leaps in your approach to the sould that are unwarranted.
1) Emergent theories of self are not 'bundle' theories even though they do admit that there are lower processes that constitute the soul itself. So 'single cause' vs 'bundle' as a dichotomy is not clean and does not cover the range of options.
Like the cells, the soul can have parts that seem to make it up, yet do not totally explain its entirety no matter how you put them together.
2) Good 'bundle' theories do not necessarily involve any misinterpretation.
Like the members, even if the soul is woven together out of perceptions and labels, it serves a purpose they would not serve on their own without the 'weaving'. So there is something to be seen there with more structure than a simple collection.
So these two concepts, emergence of function, and holistic effects, undercut the idea that the soul must be either single, or separable. The soul may be neither single, nor separable, in the same way as the body: it has parts and aspects, but if you remove a few, it is no longer a body, but a corpse.
I would propose there are at least five plausible constructions of the soul, motivated by historical precedents and an elemental breakdown along the lines of Aristotle's four causes:
1) (Quintessential) The soul's naive view of itself is as a 'single substance'. (A la Spinoza, Descartes, et al.)
2) (Formal) The soul is a collection of separate 'substances' that work together, which give it internal boundaries and psychological structure. (A la Plato and neo-Platonists.)
3) (Efficient) The soul is an emergent effect of self-observation, maintained by intersubjective feedback. (The emergentist view. Can be projected onto threads like Desassure, Wittgenstein, et. al, but they avoided speaking in these terms.)
4) (Final) The soul is a functioning entity capturing will and intention, either evolved or designed for this purpose of its own continuation. (A la later psychoanalysts, Nietzsche, et al.)
5) (Material) From a totally third-party point of view, the soul is a confluence of activities and patterns, and nothing more. (The 'bundle' views.)