Are Aristotelian non-mental ends really compatible with Brandomian normativity in an account of the same things? I want to say yes.
Aristotelian ends have frequently been read as somehow pre-existing. Later commentators in the Greek, Arabic, Hebrew, and Latin traditions certainly most often took such a view, but in so doing they were more faithful to the values of neoplatonic or traditional monotheistic theology than to the Aristotelian text.
Aristotle pioneered the idea that ends come first in the general order of interpretation relevant to life. I see this as ancestral to Brandom’s idea that normativity comes first in the same context, even though Brandom himself does not really engage with pre-modern philosophy. Brandom’s main source for this is his reading of Kant and especially Hegel, but Hegel is also the modern author who began the restoration of Aristotle to his proper place in the history of philosophy.
To come first in the order of interpretation and explanation is not necessarily to pre-exist. Consideration of the order of explanation is after all only relevant to processes of explanation. Aristotle, Kant, Hegel, and Brandom are all very process-oriented.
Brandom, drawing on Kant and Hegel, offers a broadly pragmatist account of the objectivity of values and reality, in terms of a counterfactual robustness of practical judgments ultimately grounded in mutual recognition and an ongoing commitment to the repair of errors. Such an account of a process of truth-and-error provides for everything involved in the normative sense of what we call objectivity, while making pre-existing truths superfluous.
In a much simpler but still very nuanced way, Aristotle often informally refers to existing realities. He usually starts with an optimistic and charitable approach to the deliverances of common sense in everyday life, only refining and superseding them as the need arises, but epistemic modesty prevents him from turning these into strong theoretical claims. Dialectic — i.e., exploratory discursive reasoning about concrete meanings in the absence of initial certainty — rather than demonstration from presumed truths is the main theoretical tool actually employed throughout Aristotle’s works.
On a more theoretical level, Aristotle provocatively suggests that something need not have actual existence in its own right in order to deeply affect the shape of reality (see The Importance of Potentiality). I take Aristotelian ends to be things of this sort.