> But that doesn't take into account the actual arguments involved, the doctrinal context, or how our atonement is accomplished and its consequences for our practical lives.
It explicitly does. I suggest you read Gustav Aulen's book Christus Victor
I was mainly speaking to the different theories of atonement i.e. satisfaction, PSA (boo hiss), Christus Victor, recapitulation, incarnation, Girardian etc... So you say Jesus died for our sins, whereas I would be more inclined to say that Jesus died because of our sins.
There are lots of different ideas about salvation and how salvation works and the vast majority have roots in very old traditions. For instance the idea of Theosis (prominent in the Eastern Orthodox tradition) has roots going back to Gregory of Nyssa (it probably goes farther back but I know for sure Gregory mentions it).
if you really want to know more about Atonement/Soteriology here are some resources: Christus Victor by Aulen
Jesus Humanity and the Trinity by Tanner
I See Satan Fall Like Lightning by Girard
Anselm of Canterbury: The Major Works, specifically cur deus homo
And a bunch of these multiple perspective books
There's even a pretty decent book defending PSA even though I don't agree with the conclusions the author reaches.