I do not think that there is any issue with viewing signification as an activity, in fact this is how pragmatists view it since Peirce. In modern terms, pragmatism asserts semantic and epistemological priority of knowledge how over knowledge that, so representation is viewed as a special kind of performance. The problem begins when we look into the status of what it is representational of. This brings up the issue of reference, correspondence to "reality", and is closely related to the realism/anti-realism divide. Szubka in On the Very Idea of Brandom’s Pragmatism speaks directly to your suggestion:
"Perhaps anything which is performed by us will count as a doing or action, and it won’t be necessary to describe it in some selected vocabulary (e.g. in physical, biological, behavioral, or functional one) in order to invoke it in understanding or explanation of propositional contentful beliefs and knowledge. However, by allowing advocates of global pragmatism such a latitude in this matter, one puts their view at risk of being easily trivialized."
Brandom in Pragmatics and Pragmatisms describes pragmatism "as a movement centered on the primacy of the practical, initiated already by Kant, whose twentieth-century avatars include not only Peirce, James and Dewey, but also the early Heidegger, the later Wittgenstein, and such figures as Quine, Sellars, Davidson and Rorty". Ryle, Merleau-Ponty, Polanyi and Dreyfus can also be added to this list. This is a big tent with plenty of room for realism, even materialism (Davidson), quasi-realism (Kant, Quine, Sellars), and anti-realism all the way (Rorty). Moreover, Dummet, who believes that representational and pragmatic aspects are too intertwined for either to have primacy, is nonetheless an anti-realist.
However, pragmatism is opposed to "intellectualism, the doctrine that every implicit mastery of a propriety of practice is ultimately to be explained by appeal to a prior explicit grasp of a principle". Since reference to a conceptualized object does involve "grasp of a principle" any description involving it can not be first in the order of explanation. So it is not that representational use "offends" pragmatists, it is rather that its representational character is in a sense moot. Let me give an analogy: classical objects are interesting and practically important formations in quantum theory, they are unsuitable for formulating the quantum theory.
Representational activities, truth-conditional semantics that articulates them, etc., are certainly rich and interesting topics, but they are secondary in semantics/epistemology. As Brandom puts it, “explicit theoretical beliefs can be made intelligible only against a background of implicit practical abilities”, it would be self-defeating to reference a pre-conceptualized ontology of said beliefs in articulating the said background. The "first" task is to describe how conceptualized ontologies are formed, then we can decide how seriously to take them, and how much, and in what contexts, to use them. Quine, who is a more sympathetic to your position kind of pragmatist, splits it this way in Theories and Things:
"The scientific system, ontology and all, is a bridge of our own making... But I also expressed my unswerving belief in external things — people, nerve endings, sticks, stones. This I reaffirm. I believe also, if less firmly, in atoms and electrons and classes."
Davidson, Quine's student, developed a truth-conditional semantics which is broadly pragmatist. See Verheggen's How Social Must Language Be? on his triangulation procedure, which ties practice to reference along the lines that you may perhaps find more agreeable.