Also, the differences between chimp and human are pretty consistent with plain increase in the volume (and number of neurons), if you control for, hmm, cultural differences.

You seem to be making a mistake that a lot of people without experience programing computers make, namely that merely adding computational power without improving the algorithm is sufficient to generate (Edit: useful) new behaviors. This is especially not the case with the kind of ad hoc algorithms evolution tends to generate. You're going to need new or at least improved algorithms, and if you're evolving new algorithms, they're going to be adapted to the environment you're evolving in.