Good post, LYN. To add Wittgenstein's perspective (and I don't want to be considered just a Wittgenstein-parrot, but you've already covered my other views fairly well, with your post): The "essence" of something might simply be its family resemblance to other things like it.
Example: The language-games all have some things in common with other language-games, but they don't have one singular thing that is common to all of them. Therefore, the search for an "essence of language", in LYN's framework, would be somewhat futile. However, these similarities that they share among each other make up the "family resemblances" of Wittgenstein's philosophy on language, and can thus be considered something akin to language's "essence".