This is very well written and very well thought out, perhaps the most intellectually engaging philosophy I've read on Medium since my recent arrival here.
Purely for sake of discourse, I'm tempted to say the issue you focus on is not an either-or but more of a spectrum. Kant certainly moved the needle in the direction you advocate for, and his insight appears widely recognized.
Your critique of the British empiricists certainly finds their soft underbelly. Perhaps a more sympathetic reading would be that while intellect allows us to notice and process similarities and differences, this faculty might potentially be close to useless without multiple sensory experiences to compare in the first place.
Personally, I see the idea of dog as an aggregate of all dog experiences. The intellect binds them, but it doesn't add "content" or further insight. As an analogy, a molecule has properties different from its constituent atoms, but if you "look inside" the molecule, you only see atoms -- what distinguishes the molecule are emergent characteristics.
Also personally, while we are "more than animals," too much evil has been wrought in this world by thinking we are that much more than, say, other mammals, that our intellect is as spectacularly powerful as many believe. I like the humility of thinking that, if we are superior to other mammals, we aren't much more superior, that at the end of the day, we have our limits, and when we try to exceed them, we can mess things up.