Contributions to Philosophy, Derrida and the "other beginning"

There is perhaps no better way to characterize Derrida's thought than the way Heidegger characterizes his endeavor in his Contributions to Philosophy: that is, as a "crossing over to the other beginning" (3). The other beginning--that is, of Western thought. This beginning is, as Heidegger says in his lecture on "Hegel and the Greeks" (within his book Holzwege, or Pathmarks), is not a beginning and is a beginning at the same time: it is what has remained unthought and presupposed even in the beginning of the Western tradition of thinking. In other words, crossing over to the other beginning of Western thought means not naively beginning again but rather thinking that "to which we are not sufficient [in our thinking] and never have been" ("Hegel and the Greeks"), the withdrawing-movement of Being that gives Being, Ereignis or enowning. Or, as Heidegger himself puts it: "reverence for the first [i.e. forgotten] beginning... must coincide with the retlentlessness of turning away from this beginning to an other questioning and saying" (5).
I say that this phrase "crossing over to the other beginning" exactly characterizes Derrida's effort because it is really what the phrase "deconstruction" means, primarily through its emphasis on construction. Derrida no doubt used the term because it is similar to what what Heidegger occasionally used to explain his philosophical effort of decentering the tradition of Being as presence--a positive "Destruktion." But what is really meant, as Heidegger shows us, is a thinking of the forgotten: it bringing this forgotten to the fore that will enact the "Destruktion" of metaphysics as the metaphysics of Being as presence. As such, by the link we have already established, it is a return to the origin of the origin, the beginning of the beginning, the non-beginning that is the beginning of beginning, the "other" beginning.
And the otherness of this beginning is primarily Derrida's stress throughout his career. While Heidegger probably focused on it more as a beginning, as a presupposition that the beginning of Western thought left behind and yet brought with it everywhere since Parminides, Derrida wanted to find out, and cross into himself, the otherness of this beginning and to think from it. That is, he not only wanted to think from its standpoint (which would be of necessity a non-metaphysical standpoint) as a beginning, he not only wanted to found the task of thinking on this forgotten beginning, but he wanted to think from its standpoint as other, found philosophy as a thinking within the otherness of this beginning, to the maximum possible extent. Thus Levinas remains crucial for him throughout his career.
But perhaps describing deconstruction as a "crossing over to the other beginning" of philosophy would help us think through Derrida's work in a more honest way, and render ourselves able to concretely demonstrate the positive character of deconstruction--that is, what it does that exceeds powerful critique, namely, establish philosophy in this other beginning.