I'm just trying to flesh out the arguments and the associated reasoning.
Yep - that is all any of us can do.
As for "type of matter" I am not recalling much specific at this moment, but there's definitely the references in Lucretius to the soul being made of particularly smooth and small (?) types of atoms - but that in no way implies that there is anything supernatural or eternal about it. So while the structure of such beings definitely seems to play into how they maintain themselves and replace their atoms indefinitely, I don't think anything supernatural is implied any more than the structure of the human soul which allows us to be intelligent implies anything supernatural.