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In English, we use the prefix meta, e.g. in metalanguage, to mean that something is one level higher or more abstract.
I read in the preface of a book about the software Metapost that it was a mistake based on a misunderstanding of the title Metaphysics by Aristotle, it was just meant to be the book after Physics, not a more abstract thing.
I wanted to know if this was correct, and if so, if archi- was a better Greek prefix to express this idea when coining words in Latin.
From what I learned in my bachelor's programme of philosophy, your etymology of meta- is correct, and I have also read this elsewhere. But I have not studied the term myself. It might kind of work to have the intended meaning, though only if it is read as short for metaphysical; I would say that reading is less than felicitous.
Archi- would be related to Greek archê "beginning, first principle, sovereignty, power". I think the sense "first principle" is probably mostly limited to a philosophical context, but I don't see why it could not be extended. However, there exist many words using arche-/archi-/archo- (aequivalent forms) meaning "first in time" and "most powerful", so it might not always be read the way you intended it.
I think the most logical praefix would be Latin super, though, which means "over, above". In Greek, that would be hyper-, which is etymologically related. Cf. superorder in biology, which is a higher order in taxonomy; and hyperonym, which is a "higher name", as fruit is to apple.
