UPDATE: As Eli points out in the comments, this approach doesn't seem to make sense. Saying that there is a commonality among middos does not explain our saying "Just as Avraham vanquished his Rachamim to do Your will, so too, Hashem, vanquish Your Din to do Rachamim." The point of the tefilla is that they are different and just as Avraham put the one aside to do the other, so too Hashem should.
Sometimes, the ideas that occur to me have some element of truth, although it takes time to divine what that truth is. But working on a post facto rationalization motivated by a presumption of infallibility is repugnant, so I'm putting this on the side. From what I've seen, this repugnance diminishes with increasing age, so maybe I'll come back to it.
As it turns out, this might be what Rabbeinu Bachay means in Breishis 18:33, where he says
1. See also Rav Kook's Ein Ayah, where he says
כן יכבשו רחמיך את כעסך מעלינו