Did Heidegger Read Kant's Transcendental Dialectic?

In the midst of an admirably even-handed consideration of the early Heidegger's auseindersetzung with Kant, David Carr makes a fleeting observation about how the intensive probing of that hermeneutic confrontation also  happens to be exclusive of an extensive reading ---even, in fact, exclusive of the entire extent of the first Kritik upon which it is focused:

One thing that strikes readers of Heidegger on Kant in these writings is that his analysis is very detailed and close to the text, but it is focused entirely on the first Critique and indeed goes no farther than the first third of that work. He has almost nothing to say about the “transcendental dialectic”and its critique of traditional metaphysics, in which the first Critique culminates, much less about Kant’s moral philosophy, for which the first Critique is preparing the way.

Carr doesn't stop with this somewhat blunted criticism, however. In what is an appraisal in all other ways self-restrained, Carr permits himself the following anomalously pointed remark: "...I have to wonder, in all seriousness, if Heidegger ever got as far as the paralogisms in his reading of the first Critique." The implication of Carr's speculation is clear: even in terms of its sources, Heidegger's reading of Kant is a narrow, lopsided one.
  In the present post, I want to take the opportunity to briefly suggest one reason why this is so --- why, that is, it is far from a matter of accident that Heidegger devotes himself exclusively to the Transcendental Aesthetic and Analytic in the majority of his Kant interpretations. As an aside I would allow the remark that Heidegger did not read other parts of Kant's corpus to pass as a piece of rhetorical hyperbole, were it not for the fact that even hyperbole does not allow itself to contradict historical fact (there is no need to waste breathe justifying Heidegger here on this point, he marshals so much evidence in the copious cross references he makes to the entirety of Kant's corpus ---nevermind the Dialectic). It might have been a nice addition to his Kant interpretation if Heidegger had produced, say, a phenomenological, or later, a seynsgeschichtliche interpretation of the Dialectic, one that is not altogether inconceivable in what its outline would have looked like, but Heidegger did not do so for, I would argue, a rather simple structural reason. One need only consider the architectonic of Kant's first Kritik to supply himself with the readily available answer.
   While the arrangement of the Kritik's Doctrine of Elements  can be regarded, as the Prolegomena in fact does regard it, as an arrangement of increasingly comprehensive pure foundations for the sciences of mathematics, physics, metaphysics respectively treated under the Aesthetic, Analytic, and Dialectic, nevertheless the work's arrangement can also be regarded from another vantage point. If in the former regard it is the Dialectic that treats of the possibility of metaphysics as an actual science, then in the latter regard it is the Transcendental Logic as a whole that furnishes the reader with the principles for a science of metaphysics as Kant alone wishes to establish it. This double vantage point is inherent to the work itself and may be explained by the fact that the pure physiological principles of the Analytic are at the same time metaphysical, since for Kant they ground any possible gegenstandsbeziehung.   In the order of presentation, then, the Analytic is designed to take over exactly that place reserved by Scholastic thought for metaphysica generalis, while the Dialectic is to occupy the place of metaphysica specialis. That this is so according to the rule of the work is made all the more obvious by the fact that the Dialectic's threefold division of paralogisms, antinomies, and Transcendental Ideals mirrors precisely the threefold division of metaphysica specialis into the specific domains of soul, world, and God. And it is precisely in this superficial observation of the works arrangement that we have a strong indication of the reason for Heidegger's focus. Months before Heidegger gives his phenomenological interpretations of the first Kritik, Heidegger is introducing to his students, in the Grundprobleme lectures of 1927, the problem of ontological difference, and he is doing so precisely through a destruktive meditation on Kant's categories of modality as they circumscribe the bounds of real predication. Although Heidegger had previously penetrated the Transcendental Analytic before the Phenomenological Interpretations in his 1925 Logik lectures, there it was self-evident why his examination had to limit itself in range and scope. By contrast the Phenomenological Interpretations, like the controversial Kantbuch that followed it, stood in need of some justification, and the Grundprobleme proffer that in linking the interpretation of Kant with the elaboration of the ontological difference.
     This link is of direct importance to the issue of Heidegger's attachment to the Analytic because it is as a consequence of the ontological difference that Heidegger will sever the possibility of doing anything like a metaphysica specialis from ontology properly understood. A properly ontological science will begin, as all metaphysica generalis attempt to do, with the question of Being as such. But, as the Grundprobleme make clear in their introduction, the method by which such a beginning is to be made consists in enacting a phenomenological reduction ---one which is vastly different from the move Husserlian phenomenology acknowledges by that name. In fact, precisely what was allegedly bracketed in Husserl's reduction is what is shifted toward in Heidegger's, namely Being as an antecedent given (seinsverstaendnis) which precedes and enables ontic datum:

We call this basic component of phenomenological method - the leading back or reduction of investigative vision from a naively apprehended being to Being phenomenological reduction. We are thus adopting a central term of Husserl's phenomenology in its literal wording though not in its substantive intent. For Husserl the phenomenological reduction, which he worked out for the first time expressly in the Ideas Toward a Pure Phenomenology and Phenomenological Philosophy (1913), is the method of leading phenomenological vision from the natural attitude of the human being whose life is involved in the world of things and persons back to the transcendental life of consciousness and its noetic-noematic experiences, in which objects are constituted as correlates of consciousness. For us phenomenological reduction means leading phenomenological vision back from the apprehension of a being, whatever may be the character of that apprehension, to the understanding of the Being of this being (projecting upon the way it is unconcealed).   

Heidegger's self-comparison with his mentor here is particularly instructive in the task of clarifying Heidegger's reading of Kant's Kritik; the explanation (and/or justification) of object-constitution in light of transcendental consciousness has its roots in Kant's Analytic as it is usually interpreted. If an interpretation of the Kritik is to be a phenomenological  interpretation, then it will presumably have to enact the step required to initiate any phenomenological research, namely, Heidegger's onto-phenomenological reduction. But that reduction, which serves to properly raise questions traditionally belonging to metaphysica generalis, precludes the establishment of metaphysica specialis, since, insofar as it investigates three specific (domains of) objects, the latter would be a reversal of the reduction, moving from Being to beings --a move that can only be permitted if the ontological difference remains misunderstood as a difference. Heidegger's reduction is accordingly a recapitulation of the ontological difference contra to  yet presupposed by the difference between genus and species, and therefore also problematic for the difference between metaphysica generalis and metaphysica specialis. To be more precise, the reduction shows, through the view that it enacts, a difference already present in the domain of metaphysica generalis, prior to its own demarcation from metaphysica specialis. This ontological difference, as the phenomenon which makes possible any science capable of investigating positive data, renders the three specific objects of metaphysics, namely soul, world, and God, as subject to this further unaddressed ontological difference. Soul, world and God have always been interpreted according to an already established metaphysica generalis in order to be secured as objects of investigation --and even when that security is problematized, it is done so only by what is accomplished beforehand by metaphysica generalis ---just as Kant's Analytic supplies the ground for his paralogisms, antinomies, and Ideals. In short, general metaphysics must settle itself and stabilize its fundamental principles before specific metaphysics can commence.  But if one is to, as Heidegger's phenomenological reduction would have it, demonstrate a difference problematizing the ability of metaphysica generalis to come to rest and thereby lay the foundations of metaphysica specialis, then he will also have to read the Analytic in such a way that makes it incapable of dispatching with further consideration of its subject matter in order to then transition to the Dialectic.  The phenomenologically reduced Analytic will be the
beginning of an inexhaustible perplexity.