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.
Scott Aaronson has a new 85 page essay up, titled "The Ghost in the Quantum Turing Machine". (Abstract here.) In Section 2.11 (Singulatarianism) he explicitly mentions Eliezer as an influence. But that's just a starting point, and he then moves in a direction that's very far from any kind of LW consensus. Among other things, he suggests that a crucial qualitative difference between a person and a digital upload is that the laws of physics prohibit making perfect copies of a person. Personally, I find the arguments completely unconvincing, but Aaronson is always thought-provoking and fun to read, and this is a good excuse to read about things like (I quote the abstract) "the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb's paradox, Boltzmann brains, algorithmic information theory, and the Common Prior Assumption". This is not just a shopping list of buzzwords, these are all important components of the author's main argument. It unfortunately still seems weak to me, but the time spent reading it is not wasted at all.