"Are the cognitive scientific models of how the brain and mind work supposed to be part of that conditioning which should be dispensed with?"

No. That would be delusional. Exactly as denying that fire can one burn to a crisp or arguing that a jump from a building does not end on a pavement with a splash (just for the record, theistic delusions of entitic immortality fall into the same category).

"My writings do assume a naturalistic philosophy that takes science for granted as the source of our most objective and useful models of how things work."

We are in the same boat, then. However...

"By "consciousness," then, I have in mind how organisms become aware of their surroundings, which happens via the senses and/or the conceptual models. As a mystic, you have in mind a "deeper" sense of consciousness, but that seems to be one that questions the whole scientific enterprise."

You talk about awareness, whereas I talk about consciousness. Awareness is merely a function of brain, a filter and focal point for/of mind. There is also no deeper "sense of consciousness" because that consciousness is who you are and who cognizes right now. That's how anything is known. But most importantly, it all fits into paradigms of modern science without a hitch. How could it be otherwise.

https://senderspike.medium.com/absolute-equivalence-b4584dc2e290

"I question science, too, with a pragmatic account of knowledge and with a sociological view of humanism. But I don't dismiss scientific knowledge as mere conditioning or illusion."

Neither do I, but science (and all "objective knowledge" in general) is merely a description of the mechanics of a dream. It's the knowledge of manifested causality. Functional, mostly spot on, but a dream map nevertheless.