I'm not smart enough to really think it through but at a glance it seems to resolve those various tests and scenarios. In the malfunctioning teleport example (where the cell destroyer fails to fire), _both_ London Tim and Boston Tim are equally alive because they share the past: the teleport has succeeded in bifurcating their consciousness. Same with the split-brain twins (though you'd expect the results to be diminished).
These thought experiments got me thinking about how a conscious entity might better be considered as its "world line", not just its instantaneous physical embodiment. Call that a soul if you want, but there's no particular reason to.
But we effectively always get back the the ship of Theseus, and circling back to Trek,
Does Data have a soul? I don't know that he has. I don't know that I have. But I have got to give him the freedom to explore that question himself.