I would add another point with regard to observer-moments and continuity:
probably there is no unique "next" or "previous" relationship among
observer-moments.

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The case of non-unique "next" observer-moments is uncontroversial, as it
relates to the universe splitting predicted by the MWI or the analogous
effect in more general multiverse theories. Non-unique "previous"
observer-moments can probably happen as well due to the finite precision
of memory. Any time information is forgotten we would have mental states
merge. This requires a general multiverse theory, or at least a model
of mental states that span MWI branches; the conventional MWI does not
merge branches which have diverged through irreversible measurements.
In this view, then, we can chain observer-moments together to form
observer-paths, or more simply, observers. But the chains are non-unique;
obervers can intersect (share observer-moments and then diverge), or
even braid together in interesting ways. That means that there is no
unique sense in which you are a particular observer, at any moment;
rather, you can be thought of as any of the observers who share your
current observer-moment.
Hal Finney