The situation with Incarnation theology is not as if there are a dozen theories, some of which seem more plausible than others. Instead, there is only a single mantra, "Jesus died for our sins," which is as meaningless and incomprehensible as "Jesus painted for our hubcaps."
This particular phrase has destroyed the discernment of more Christians and has been responsible for more atheists than any other unreflectively accepted proposition of Christianity.
The first merit of my own theology is that it is not the case that it does not make a lick of sense.
The second merit is that it actually makes a good deal of sense by explaining adequately what happened and why.
The crucial question is, "What was God trying to achieve by incarnating?" My theology answers it; the "traditional" cant about "sacrificial lamb" does not.
The sacrifice theology goes like this: the Father was fed up with the world and about to pull the plug on it and execute everyone. The whole universe with stars and planets and tables and chairs was about to disappear, as the Father was preparing to wipe everyone out.
Then the Son intervenes and says: No, no, no, I love those guys. Don't kill them. Kill me instead.
The Father says: Well, I've got to kill somebody, I'm in the killing mood, so fine, I'll kill you. And now I am feeling particularly mean, so you'll die most unpleasantly, too. Go get yourself crucified.
Does that sound that like the sort of way God would act? It most certainly does not.
Is it possible that the Father wanted to test the Son's love for us? "You can save the world from destruction by me if you agree to be destroyed in its stead." This explanation has inched very closely to my own, but it's still inadequate for failing to explain the Son becoming man. Surely, the Father could have slaughtered the Son in His own self rather than go through a massive amount of highly peculiar trouble to get His human body killed by us.
In fact, I contend that the Son died and was reborn not once but three times for the sake of the world: before creation to get His intellect uplifted; at birth for the sake of power; and on the cross to decide whether to accept the charity in His will for humans. Why wasn't the first death enough for the Father? I think it was. The Son's second death was at the hands of the Holy Spirit, as per "The Holy Spirit will come on you, and the power of the Most High will overshadow you. So the holy one to be born will be called the Son of God." (Lk 1:35) That's the "kenosis." And His final death was due to our human actions.
Jesus had to choose whether to condemn or redeem us in light of our ultimate act of violence against Him personally. That He chose to redeem, i.e., to connect humanity to the Father through Himself as branches to a vine, was a contingent event; it did not have to happen; the fate of the world hanged in the balance as Christ was contemplating His decision. Jesus was not simply going through the motions, where everything was already known and predestined; though He may have foreseen His course of action, He still freely chose it, and it is for that choice, in our favor, that we glorify Him.
In short, Jesus proved His love for us both to the Father, to the Holy Spirit, and to mankind.
We might say that the devil challenged the Son, and the Father refused to believe that the Son "loved" mankind without the trial or gauntlet of Incarnation. The Father would not allow humanity to be part of the divine family unless He could verify beyond the shadow of a doubt that the Son's claim to love us humans was not mere words on the Son's part. In this sense, we could say that the Father "did not spare" His own Son.
Is my soteriology "the protracted tale of the brinkmanship of God"? But don't you feel the drama? The burden both thrown on us and taken up by God? Life is not a game, where God leisurely supplies a happy ending for everyone. No happy ending was ever guaranteed. Lucifer bet both against us and against God the Son. Even the second bet was real, and the devil thought he had a non-zero chance of winning. He lost. The first bet is still on, however.