Annihilation of ”mere cessation” ;)

But if one can still perceive beyond the dimension of neither perception nor non-perception, why is this all of a sudden impossible just because the death of, such a trivial thing, as the physical body?

How can even anyone know this for sure that with parinibbāna this immersion beyond existence becomes impossible?

You have no way of proving that parinibbāna is different in regards to this.