While Wright is pegged as the “ecclesiological” version of justification, it strikes me that this is a red-herring. While justification as covenant status addresses the division of Jews and Gentiles, the problem is more basic. Wright sees justification has addressing the human problems of sin, condemnation, and death, and Paul’s discussion of a creational, anthropological, covenantal, and forensic eschatology is described in terms of justification (see the progressive discussion of these framing terms in Paul and the Faithfulness of God, 925-37). Ultimately this is all captured in his discussion of final eschatology:

Paul’s vision in Romans 1-8, then, has as its framework the all-important narrative about a future judgment according to the fullness of the life that has been led, emphasizing the fact that those ‘in Christ’ will face ‘no condemnation’ on that final day (2.1-16; 8.1-11, 31-39). The reason Paul gives for this is, as so often, the cross and the spirit (8.3-4): in the Messiah, and by the spirit, the life in question will have been the life of spirit-led obedience, adoption, suffering, prayer, and ultimately glory (8.5-8, 12-17, 18-27, 28-30). This is not something other than ‘Paul’s doctrine of justification‘. It is its outer, eschatological framework.   …   And, to repeat a vital point about the character of Paul’s theology, that integration [of present and final justification] makes nonsense of all schemes that depend on regarding Romans 1-4 and 5-8 as representing two types of thought or systems of soteriology. That division results from failing to notice Paul’s larger controlling category, namely, the covenant promises made by God to Abraham to deal with the problem of the world’s sin and its consequences. Those, Paul insists, are the promises to which the covenant God has been true in the Messiah. The faithfulness of this God is the underlying theme of Romans 1-8… [sic] as it is also the problem, and then the solution, throughout Romans 9-11. (Paul and the Faithfulness of God, 941-42)

He later uses the terminology of ‘inaugurated forensic and covenantal eschatology’. “The future verdict … is thus brought forward into the present, because of the utter grace of the one God seen in the ‘faithful’ death of the Messiah … and then at work, as we shall now see, through the spirit in the gospel” (944-45).

Restoring the community, setting it to rights, is important, but in Christ and the Spirit God is setting the whole world to rights, and so to limit justification, for Wright at least, to ecclesiology is to miss his larger picture. That said, he frames it this way:

Once we have worked through the first five preliminary points, we ought to realize that this sixth one is where it has all been going. Those who are declared or accounted ‘righteous’ on the basis of Messiah-faith constitute the single covenant family which the one God has faithfully given to Abraham. (Paul and the Faithfulness of God, 961)