on second reading of the relevant section of the kaku book (pp 144-150), I guess my guesses are a ways off, and it sounds like supergravity has problems anyway.
still, I wish I could find some sort of conceptual pegboard to put ideas on as I learn them, a whole that I could relate each new...
attached are figures taken from greene's fabric of the cosmos and kaku's hyperspace. greene's depicts a calabi-yau manifold at each spacetime point, and kaku's seems to suggest a kaluza-klein-esque combination of forces (he might have been talking about supergravity, I don't remember now)...
my (effectively undergraduate) understanding is that with E&M as 1 KK dimension, velocity in this extra dimension corresponds to charge density.
in the un-unified formulation you mention, do velocities in these extra dimension correspond to hypercharge and colors perhaps? perhaps with 2...