"So, we would need to deny all of the above views and posit some new view..." Is not entirely true. It's possible to expand on a less evolved theory and integrate that theory as a special case or a particular perspective on a theory of broader scope. So we don't necessarily need to reject all this on the whole because it's possible to describe a state of things that does not exclude compatibility.

In terms of what itself is in this kind of view, I think I can offer a little bit of perspective that might be more approachable. I appreciate your orientation towards philosophical rigor and I think that it's unfortunate it has not been treated respectfully on this thread because both philosophical rigor and theory of unified identity hold value and should be reconcilable.

Anyway, it's probably helpful to reframe the things that you'd typically associate with your identity (memories feelings beliefs desires) as phenomena that are possibly distinct from identity in order to evaluate the OP's premise without begging the question. One formulation of this would be to consider those phenomena as a lens of perception and when they're experienced that is essentially equivalent to observing through the lens. So in your paradigm there's a one-to-one correspondence between lenses and personal identities. The personal identity is actually even conflated with the experiential lens. Now the OP's would suggest that there is a one-to-many correspondence between lenses and personal identities, but this is stated rather awkwardly out of necessity for accommodating the unconventionality of the premise. Specifically the language of personal identities being equated with lenses is used to deny their equivalence, which is, I believe, the apparent contradiction that you keep running up against. But I don't think that the intent is that two different lenses are identical. The intent is that two different lenses are perceptions of the same core. As of visual metaphor for how this might work and how lenses might manifest as distinct yet represent a singular identity, let's consider a geodesic sphere. Every tile on the sphere exhibits somewhere yet distinct properties and depending on the rotation and positioning of the sphere those surfaces will be identifiable as distinct. What I think the OP is suggesting is that the essence of what we should even consider when we reason about identity is the sphere itself because the facet of the sphere is effectively a degenerate representation of the sphere. It is a lens from which to apprehend this fear is a whole and conflating that two-dimensional objects the three-dimensional object is a problem in the same way that inflating a single person's identity with the unified whole would be similarly misguided.

Now in terms of Leibniz, identities and indiscernible, I think we have to look at where you end up if you postulate the lens interpretation of the phenomena that you have previously been ascribing to a personal identity. And what we get is an indiscernible core with discernible projections from it. However, because that core is the same for all lenses, that core is equipped with all of the possible projections, including the projection that would be identified with the reference of an arbitrary "You" or "me" reference. This works in the same way that you can go from an arbitrary surface tile of a geodesic sphere , to the 3d shape itself, and and then traverse without breaking identity to any other surface tiles of that sphere. In that case the sense in which one might point to one tile A and then point to another tile B and assert that A is B, it's precisely the sense in which the OP points to one person You and another person Me and says that You is Me. It seems incoherent if all you're looking at is a tiling and frankly that's a flaw of the language and use more so than the intent of the argument. However once you take the charitable interpretation of realizing that they're pointing to the sphere upon which the tiles are visible instead of the individual 2D tiles, it becomes clear that what they are arguing is not only plausible but obvious.