Given 6*10^20 neurons in the human race, we have 10^3 atoms in 12 grams of carbon per neuron, a little bit more than 1 neuron simulation per atom. I'm not a neuron simulation or an atomic computing expert but even a few orders of magnitude above it (e.g. 1.2 kg of carbon) would give us sufficient computing power for a neuron AFAIK.

Also 10^11 neurons fit in roughly 0.001 cubic meters (i.e. a cube of 10cm), a thousand would fit in a cubic meter, your one brain simulation server room has space to a 100,000 actual human brains. Even if the simulation hardware occupies the same space as the human brain requires we would use only 0.01 cubic kilometers for the entire human race simulation. I have to agree that this will cost more than $1k, but is much smaller than your design.