Ayn Rand's egoism is untainted by any element of the mind/body dichotomy. On her view, man can achieve happiness by acting in his long-term, rational self-interest, neither sacrificing himself to others, nor sacrificing others to himself. In the long run, a man can erase conflicts within his soul, not by repression, but by an active process of rethinking the subconscious premises on which certain emotions are based. If a man lives a life of integrity -- of non-contradiction between his thought and his action -- his subconscious will have no reason to complain.
Reason and emotion are not at war, because emotions are based on intellectual value judgments, held either implicitly or explicitly. If you sense a reason/emotion conflict, what you sense is actually a conflict between two different ideas in your mind: one conscious, the other subconscious.
Politics is the study of the nature of government. In government, Plato's non-Pagan mystical aspect reasserts itself, as any vestige of egoism is dispensed with. Plato adopts an altruistic politics, one in which the individual must sacrifice himself for the whole -- this is the doctrine of collectivism.
The consistent and logical application of Platonism to life is the sort of existence which mankind experienced in the Middle Ages. In that time, men cloistered themselves away from mundane concerns, and attempted to gain insight into a higher, spiritual reality. You know what consequences this trend had.
The Renaissance represented a rebirth of reason, thanks mostly to the Aristotelian thought of St. Thomas Aquinas. Aristotelianism has always represented the antithesis of Platonism. When Plato saw forms in another dimension, Aristotle looked at the real world. When Plato sought refuge in intuition, Aristotle looked to logic. When Plato urged men to merge themselves with the collective, Aristotle stood for individualism. When Plato advocated a communist state, Aristotle advocated a sane polity, where law, not men, would rule other men. These ideas were the foundation of the Renaissance, and the subsequent periods of Enlightenment, Scientific Revolution, and Industrial Revolution.