>>gap between our (linguistic)nervous system and (linguistic) brain?

You mean periphery vs brain? I'm no expert here, but both language production and decoding appear to be in the cortex (Broca’s and Wernicke’s areas, respectively).

If you're approaching this via Minsky's hypothesis of a 'grammar structure', behaviorally there seems to be one during early language acquisition, but all attempts to find one structurally have come up empty.

Not sure what you mean by 'neurospecific bias', but non-neuronal cells appear to communicate in a bioelectric way similar to inter-neuronal communication. The Levin Lab has been looking at what role this plays in embryonic and regenerative development. If that's of interest, some of Michael Levin's presentations have made their way to youtube. Maybe start there? Some of the bioelectric work they've been doing is with planaria - the last ancestor we have in common with the octopus - to come back to cephalopods...

As far as objectivity/subjectivity and science - science is just a method to sidestep subjectivity. Couple that with Baysean reasoning and, so far, it's the best way humans have found to model the real world - and modeling seems to be the heart of how we perceive the world.