Do you believe piggys death is symbolic of the human drive towards savagery demolishing reason within a society or do you believe it represents that a lack of faith in reason among the society to begin with drives savagery?

I think your former (first reason) is closer to the truth. Golding wanted to demonstrate that that human nature, unfettered by societal rules and enforcement, is naturally drawn towards savagery and chaos. Piggy represented intellectual enlightenment: the boys' primal desires were much too strong for Piggy.