Ok, I couldn’t finish it all; however, I do have two bones to pick with it. First off, Harris focusing his knowledge in morality in such “intuition” is not him giving heed to the “inner knowledge”. He is not following the same path as Hitchens. He is following a philosophic theory called Foundationalism. It is the idea that all knowledge is based arbitrarily on fundamental ideas that within themselves are proved. Its our only means of acquiring knowledge. Now, it is on this knowledge that morality is based. So he’s not consigning knowledge of morality to our “inner knowledge” but rather he’s attributing it arbitrarily having well-being as the moral good. This assignment of fundamental knowledge is the same as the foundation of anything epistemic. Or this is how I see it at least.
Secondly, if I remember correctly, Harris propagated the idea of reciprocal altruism, not simply altruism. On this, I completely agree. Reciprocal altruism is more moral than altruism because it ensures our happiness as well as the happiness of others.