More or less I am asking for a defense of the propitiatory view of atonement in which God changes from being angry to being happy with us rather than sinners being the ones who need to change. Perhaps I misinderstand this model.
You misunderstand the model. But it's a common misunderstanding. One that comes up often enough that there's a standard answer from Apologetics. Here is is in my words:
The statement that God doesn't change means that His nature doesn't change. His Nature includes many attributes that never change: Goodness, holiness, He is Just, Righteous, and executes Judgement. None of these change.
His attitude toward us can and does change. This is not only consistent with the idea that His nature never changes, it is necessary if His nature of righteousness never changes. If God is righteous, He must punish sin. Therefore, if we are in sin, He must punish us. If He is forgiving, then His attitude toward us must be able to change from wrath to forgiveness.
I am a parent. I love my children. I will always try to do what's best for them, which means I will praise them when they deserve praise, I will punish them when they deserve punishment, I will comfort them when they are hurting, and I will burn with anger if anyone hurts them.
The fact that I can be angry with them when they are naughty and please with them when they are good does not mean that I change. I remain the same. Who I am does not change, my nature does not change. Neither does the fact that God can be angry with us, and then forgive us means that He changes.
More on this at Apologetics Press, on the question of "Does God repent?"