“From this perspective, capitalism is contradictory – but this contradiction by itself won’t “resolve” in any particular way: capitalism reproduces itself through a movement over time that is “contradictory” in something like the sense of the passages from Phenomenology above – where, in spite of an immense amount of “development” and the “overcoming” of all sorts of concrete social institutions, the same “inherent nature” still continues to play itself out, and can therefore plausibly come to be read as the “telos” of all this frenetic, coercive “becoming”. It is this “inherent nature” that needs to be overcome, from the standpoint of the sort of critique I am trying to develop, in order to overcome capitalism; and contradiction, within this framework, is the means of the reproduction of a particular society, rather than a way in which that society points beyond itself.”

Moishe Postone expresses a similar idea in Time, Labor and Social Domination:

“By specifying the contradictory character of his own social universe, Marx is able to develop an epistemologically consistent critique and finally to move beyond the dilemma of earlier forms of materialism he outlined in the third thesis of Feuerbach: A theory that is critical of society and assumes humans and, therefore, their modes of consciousness to be socially formed must be able to account for the very possibility of its own existence. The Marxian critique grounds this possibility in the contradictory character of its own categories, which purport to express the essential relational structures of its social universe and, simultaneously, to grasp forms of social being and of consciousness. The critique is thus immanent in another sense: showing the nonunitary character of its own context allows the critique to account for itself as a possibility immanent to that which it analyzes.” (143)

Postone mentions two kinds of “contradiction” here: the “contradictory character” of the theory’s categories, and the “nonunitary character” of the theory’s context. The former allows for an account of a social configuration from within that configuration, and in just the manner you outline; while I think the latter points to the possibility of an alternative social configuration through the fact that critique is the product of a historical consciousness bound to a particular configuration, and thus “the historical overcoming of capitalism would also entail the negation of its dialectical critique.” My hunch is that these might correspond to the two senses of contradiction you list respectively.