what could there be beyond the causal stuff?

Maybe my basic point is that there is more to the "stuff" than just "being causal". This is why I talk about abstracted causal models as ontologically deficient. Describing yourself or the world as a state machine just says that reality is a merry-go-round of "states" which follow each other according to a certain pattern. It says nothing about the nature of those states, except that they follow the pattern. This is why functionalist theories of mind lead to patternist theories of identity.

But it's clear that what we can see of reality is made of more than just causality. Causal relations are very important constitutive relations, but then we can ask about the relata themselves, the things connected by causality, and we can also look for connecting relations that aren't causal relations. Being shaped like a square isn't a causal relation. It's a fact that can play a causal role, but it is not itself made of causality.

These are ontological questions, and the fact that we can ask them and even come up with the tentative ontologies that we do, itself must have ontological implications, and then you can attempt an ontological analysis of these implication relations... If you could go down that path, using beyond-Einsteinian intellectual superpowers, you should figure out the true ontology, or as much of it as is accessible to our sort of minds. I consider Husserl to be the person who got the furthest here.

One then wants to correlate this ontology derived from a phenomenological-epistemological circle of reflection, with the world-models produced in physics and biology, but since the latter models just reduce to state-machine models, they cannot in themselves move you beyond ontological hollowness. Eventually you must use an ontology derived from the analysis of conscious experience itself, to interpret the formal ontology employed by natural science. This doesn't have to imply panpsychism; you may be able to say that some objects really are "things without an inside", and other objects do "have a subjectivity", and be able to specify exactly what it is that makes a difference.

This is a little removed from the indexical problem of

why am I me, and not someone else?

That's a question which probably has no answer, beyond enumerating the causes of what you are. The deep reasons are reserved for why there is something rather than nothing, and why it is the sort of universe it is. But in a universe with many minds, you were always going to be one among many.

If you were to find that the nature of your personal existence looked rather improbable, that would revive the question a little. For example, if we thought electrons were conscious, then being a conscious being at the Avogadro's-number-of-electrons level of organization, rather than at the single-electron level of organization, might look suspiciously improbable, given the much larger numbers of electrons in the universe. But then the question would be "why am I human, and not just an electron?" which isn't quite what you asked.

I think, therefore "something" is

I agree with this part.

The universe doesn't care whether I landed in vulcan by shuttle or by energy beam, it's the same configuration.

I think what you're saying is that in the present, there's no difference between your current configuration having resulted from a life lived for 20+ years, and your current configuration having materialized five seconds ago. Well, if by hypothesis the configuration is exactly the same in the two scenarios under consideration, then the configuration is exactly the same. That much is true tautologically or by assumption.

Now if we ask whether it's "still you" in both cases - one where you live out your life with physical continuity, and one in which you are briefly eradicated and then replaced by a physical duplicate - you do have some freedom of self-definition, so the answer may depend a little on the definition. (For now I will not consider the Yudkowskian possibility that there is a unique correct definition of personal identity to be found by superintelligent extrapolation of human cognitive dispositions, analogous to the CEV theory of how to arrive at a human-correct morality.)

But there are obvious and not-so-obvious problems with just saying "the configuration's the same, therefore there's no difference". An obvious problem: suppose we make more than one copy of you - are they both "you"? Less obvious: what if the history of how the configuration was created does matter, in deciding whether you are the same person as before?

Does "having the memory of being in a green room" really imply "you have been in a green room"? We don't normally trust memory that absolutely, and here we are talking about "memories" that were copied into the brain from a blueprint, rather than being caused in the usual fashion, by endogenous processing of sensory input. It is reasonable to imagine that you could be that person, whose brain was rewired in that way, and that after reflecting for long enough on the situation and on how the process worked, you concluded that it wasn't you who was in that room, or even that nobody was in that room.

I'm not even convinced that the unlimited capacity to recreate a whole conscious mind "in midstream", implied by so many thought-experiments, is necessarily possible. There are dynamical systems where you just can't get to places deep in the state-space without crossing intermediate territory. If all that matters for identity is having the right ensemble of mesoscopic computational states (i.e. described at a level of coarseness, relative to the exact microphysical description, which would reduce a whole neuron to just a few bits), then it should be possible to create a person in mid-stream. But if the substrate of consciousness is a single quantum Hilbert space, for some coherent physical subsystem of the brain, then it's much less obvious that you can do that. You might be able to bang together a classical simulation of what goes on in that Hilbert space, in mid-stream, but that's the whole point of my version of quantum-mind thinking - that substrates matter, and just implementing a state machine doesn't guarantee consciousness, let alone persistence of identity.