Do I understand it correctly that the question is, essentially, whether there exists a more efficient way of modelling the brain than modelling all particles of the brain?

I don't presume to speak for Scott, but my interpretation is that it's not a question of efficiency but fidelity (that is, it may well happen that classical sims of brains are closely related to the brain/person scanned but aren't the same person, or may indeed not be a person of any sort at all. Quantum sims are impossible due to no-cloning).

For more detailed questions I am afraid you will have to read the paper.