With regard to "mental", it seems to me that word is standing in for a whole class of things that aren't simple and mechanical. An ontologically basic architectural or legal entity sounds like it should qualify as supernatural, as does an ontologically basic dead rat.

1) In "Excluding the Supernatural", Eliezer says:

Ultimately, reductionism is just disbelief in fundamentally complicated things.

I think this version of the definition includes more of what we think of as "supernatural" without including anything that we wouldn't. Under this definition, an ontologically basic dead rat would be supernatural, as I think it should be. Of course, this is assuming I have anything like a correct picture of what you mean. I can't really envision an ontologically basic dead rat, but neither can I see what good it would do me to do so.

2) The phrase "ontologically basic dead rat" is surprisingly funny.