That's just restating the circular approach, and continuing to look at it from a specific medical approach.
I don't think it is a circular approach, merely using the definition of death. And surely any meaningful definition of death relates to the end of life, which is in itself defined in terms of ongoing biological processes.
If there is such a thing as consciousness extending beyond what specific line we can draw at any time as the 'irreversible' bit, then using the term in the way you do makes discussion impossible. Given that billions believe that consciousness does extend beyond death then it seems difficult to have a discussion about why one thinks they are wrong by pointing to a definition that they don't accept.
But isn't that the issue - that there are those that consider that consciousness is able to continue following the irreversible cessation of physiological/neurological processes (i.e. death), thereby decoupling consciousness from biology. That would certainly appear to be the view of many religious people, not least the likes of Sriram and AB on these boards. Now I don't think there is any evidence for this whatsoever, but that is surely their argument.
Now following on from this, were someone's consciousness to be able to communicate to others despite an irreversible cessation of biological processes then this would be 'after death' - some people think this can happen - I've seen no credible evidence for this. However if someone is resuscitated and those biological processes have not irreversibly ceased then there has been no death and whatever they may tell you cannot be an experience of death, because they were never dead.