Wright's argument is stronger when he comes to Romans. He looks at 3:21-26, 10:2-4, and 1:16-17, and his distinction comes into clearer focus - that is, Wright's distinction between God's own righteousness (His being true to His word and His ruling justly) and the righteousness by which we are cleared of guilt and can come before God. Romans 3:25-26 makes this point very clearly - that Paul is talking about the former, not the latter, righteousness - God's own. Jesus' death on the cross clears a shadow on God's reputation as a just judge. He had left so much sin unpunished, Israel was beginning to wonder. But now it's all clear: ALL have sinned (Israel too) and are made righteous through Jesus' sacrifice.
Wright wants to emphasize God's own righteousness, because he wants to avoid seeing our salvation as a merely forensic and legal transaction. This obscures the love of God, which drove Christ to the cross in the first place. And I agree completely, as long as we don't end up denying that to be spared God's wrath, we must have a righteousness not our own, reckoned (imputed) to our account. But absolutely, love motivates the transaction.
D.M. Lloyd-Jones makes the exact same point in a Banner of Truth booklet, "The Cross: The Vindication of God," more than 40 years ago. There's nothing new here.
So Wright's point is that Paul's phrase "righteousness of God" doesn't refer to our acceptable standing before God, but to God's own righteousness. But when he comes to Romans 1:17, I think I have a problem. "For I am not ashamed of the gospel of Christ, for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek. For in it the righteousness of God is revealed from faith to faith; as it is written, “The just [righteous] shall live by faith.” Wright makes a strong distinction between God's righteousness and our own. Paul talks most about the former, Wright says. But this strong distinction misses something here in 1:16-17. Vs 16, I agree, Paul is talking about God's own righteousness, but then he elaborates on it by quoting Hab 2:4, which appears to me to refer to the righteousness of God's people, not God's own righteousness. In other words, Paul uses righteousness in two different ways in these two verses, and uses one way to explain what he meant by the other way! That doesn't sound like a very strong distinction to me.
The whole point of the Incarnation of our Lord Jesus Christ was to bring holiness back to men, and that only God could do that. We are called to bear God's image, to be like Him. So, remembering obvious Creator-creature distinctions, the righteousness of God should be blurred a bit, as people begin to see Jesus through the mirror of our lives.