Individual wrote:... which I think falls under the phrase "post-mortem continuance." That phrase seems like a synonym for reincarnation. There is continuance of causality, but not personality
I coined the phrase "post-mortem continuance" particularly to demonstrate what I have bolded in your post above. The words "rebirth" and "reincarnation" both suggest there is something to "re"... which seems to be the thrust of Buddhadasa Bhikkhu's objections which I quoted above.
Indeed there is no "re", but that doesn't mean that the causal aspect of the four mental aggregates which continued throughout life suddenly cease to have corresponding effects, simply because what we conventionally call "death" has occurred.
Buddhadasa Bhikkhu's concern seemed to be that views of rebirth and reincarnation had the potential to blind people from the reality of anatta.