One of the benefits of reading Romans "backward" is how it helps solve some of the puzzles when we read Romans "forward."
For example, when we read Romans forward we tend to think Part 1 of the book is Chapters 1-8, where Paul's does heavy theological lifting to show how we are made righteous by faith. Part 2 of the book is Chapters 9-11, where Paul seems to take a detour about unbelieving Israel, before turning to practical exhortations and church matters in Part 3, Chapters 12-16.
Read forward in this way, Chapters 9-11 don't seem to fit well with the whole. Consequently, what Paul is doing in Chapters 9-11, and why he takes so long to do it, has struck many readers of Romans as a bit of a mystery. Sermons you've heard from Romans bear this out. I expect most of the sermons you've ever heard from Romans have come from Chapters 1-8 or 12-16. For the most part we leave 9-11 alone.
But when you read Romans backwards, following Scot McKnight, the logic and purpose of Chapters 9-11 become perfectly clear.
Recall, the "strong" and "powerful" in the Roman churches were the Gentiles. And this group was despising and disparaging of their "weaker" Jewish brothers and sisters. Given this hostility and pride Paul spends time in Chapters 9-11 to put the Gentiles in their place.
You see this most clearly in Chapter 11, where Paul reminds the Gentiles that the Story that has saved them was not their Story, it was Israel's story. Using a horticultural metaphor, Paul explains how the Gentiles are not the natural root of the Story but must be unnaturally grafted in:
If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, do not consider yourself to be superior to those other branches. If you do, consider this: You do not support the root, but the root supports you. You will say then, “Branches were broken off so that I could be grafted in.” Granted. But they were broken off because of unbelief, and you stand by faith. Do not be arrogant, but tremble. For if God did not spare the natural branches, he will not spare you either.Notice how Paul is humbling the snobby Gentiles in their treatment of their Jewish brothers and sisters: "Do not consider yourself to be superior to those other branches," "You do not support the root, the root supports you," and "Do not be arrogant, but tremble."
When we read Romans backwards, keeping Paul's pastoral concerns in view, the mystery of Romans 9-11 evaporates. We see how Romans 9-11 isn't a mysterious detour at all, but a key and central part of Paul's pastoral goal to address the Jew/Gentile conflict in the church.