Heidegger would reject the connection between rationality and authenticity. When we seek rational grounds for actions, we seek a principle beyond our finitude that can ground the justice or rightness of our activity. Kant is a primary example of a thinker who seeks rational grounds for practical activity, and is also a good example of the type of thinking Heidegger rejects with his theory of authenticity.
According to Kant, we are moral when we act not in conformity with the law, but out of respect for the law. Though the law is something we discover in ourselves, it is universal and necessary, and transcends our particularity and finitude.
For Heidegger, on the other hand, our finitude is radical and inescapable. The pretense of universal laws or principles is an escape from the responsibility for ourselves that this radical finitude demands. We are being authentic only when we act while being consumed by that finitude - without any grounding in reason.
He would also reject the correlation between authenticity and efficiency. This sounds more like the way of thought he associates with Nietzsche's nihilism and modern society's technological thought, which equates being with value. There is no sign by which one can distinguish an authentic action from an inauthentic one (interestingly, this is true of moral actions in Kant's view as well - one never knows if someone has acted out of respect for the law or merely in conformity with it). The thought of being, as Heidegger says in a later work, changes nothing.
