Don't try to refer to non-chordates as a single class, would be my suggestion. Mark chordates (and tetrapods particularly) linguistically as the unusual case instead.

What measure of complexity of the brain's organization wouldn't show a big increase between invertebrates and humans?

with a little judicious editing, becomes:

What measure of brain complexity wouldn't show a big increase in tetrapods, and humans in particular?

Biologists typically talk of chordates, arthropods, molluscs, annelids, nematodes, rotifers, etc. individually; I still suspect there is some anthropocentric bias in our taxonomy (are we really different enough from chimps to justify a separate genus?), but far less than there is in the general population.

Amusing example: At the Creation Museum, they have a chart of their taxonomy (as opposed to the standard biological taxonomy). It lists "man" as a separate category distinct from everything else, but then it ties together with a common ancestry groups as diverse as "dinosaurs", "insects", and (my personal favorite) "fungi". So the entire domain of fungi, from yeast to mushrooms, is allowed to have a common ancestor; but God forbid anyone suggest that humans and chimps are related.