Oedipus vs. the Oedipus complex?

For all the pleasures and terrors of Fagles’ translation of Oedipus the King, there would seem to be a slight disjuncture between the action of Sophocles’ tragedy and Freud’s formulation of the Oedipus complex in The Interpretation of Dreams. At least in the portion excerpted in our textbook, Freud clearly posits the (male) child’s sexual desire for its mother and jealousy of its father as the nucleus of the psychic “complex” later resolved, or not, over the course of adolescence and adulthood. Yet if Oedipus really manifested this “complex” in Sophocles’ play consistent with Freud’s theorizing, would he not instead have desired Merope and hated Polybus, his adoptive parents in Corinth and the only parents he had known since infancy? To understand Oedipus’ actions in adulthood as an accurate fulfillment or working-through of Freud’s complex, we would have to imagine that his desire-jealousy for his birth parents, Laius and Jocasta, had already fully taken root by the time they abandoned him at what the play suggests was a very early age, at most a few months old. Is it plausible that, as Freud’s complex would have it, Oedipus’ desire-jealousy survived whole, undimmed and decisive throughout the years he was being reared by Polybus and Merope and growing into manhood? Oddly enough, the Oedipus complex seems to apply to the plotting of Oedipus the King mainly as a richly suggestive back-projection from Freud’s Vienna onto an abstracted classical past, rather than by actual adherence to its operations as Freud posits them.