I have an objection to this:

So branching is the consequence of a particular type of physical process: the "measurement" of a microscopic superposition by its macroscopic environment. Not all physical processes are of this type, and its not at all obvious to me that the sorts of processes usually involved in our deaths are of this sort.

I think that essentially all processes involving macroscopic objects are of this type. My understanding is that the wave function of a macroscopic system at nonzero temperature is constantly fissioning into vastly huge numbers of decoherent sub-regions, i.e., "worlds." These worlds start out similar to each other, but we should expect differences to amplify over time. And, of course, each new world immediately begins fissioning into vast numbers of "sub-worlds."

So, while in one world you might get run over by a bus, there is e.g. another world that separated from that one a year ago in which the bus is late and you survive. Plus huge numbers of other possibilities.

In this vast profusion of different worlds, for any given death there's essentially always another branch in which that death was averted.