What does it mean to "bear our sins in his body"?
Can you "prove" a meaning from other scripture rather than just speculating?
If not (if the definition cannot be clarified in scripture) then WHATEVER we (you or I) assume that phrase to mean is our eisegesis and assumption into the verse rather than an exegesis taken out of what Peter taught.
I think that to bear our sins in his body is penal substitution and I arrive at it like you do above with the Trinity. Scripture builds a case and then you develop a theological principle. If that were not the case either we should never do theology or else the Bible would have been written in the format of systematic theology.
It is substitution in that we were bearing our sins ourselves but it is said that Christ bears them. Here's my reasoning for that part. The only way to get around this referring to a transfer of the bearing of ours sins as not meaning the taking them from us and putting them on Christ would be if we truly had no personal responsibility for bearing those sins anyway. And that is exactly what the old Socinian and some of the modern theorists assert. They do this by saying either that God simply is glad to forgive without any concept of retributive justice or cosmic justice being involved, which I believe is refuted in other scriptures. But if that were true then yes, you could say look, life is hard and we are all having a hard time down here. Jesus is only acting in solidarity with us and bearing similar difficulties, (not our sins, because that would still involve transfer) but similar or equivalent "bearing" of something as it were. If there is another meaning I would like to hear it from you, not Jon, just to get another take on this as I honestly don't understand him on this.
The other thing I would say regarding this is that what exactly is he or formally we, bearing? I agree that we can't literally bear the actual sin which may consist of an act, an attitude or word or a failing of a duty so what does it mean? It means the judged consequences and judgement of that sin, and it means the wrath that is explained in other scriptures as a holy God's reaction to such sin. That is specifically what Christ bore in his body on the tree. The suffering on the cross, the shedding of blood, the physical death, and the temporary separation from the Father is what happened there and it was as our sins were laid on Jesus.
Now, I personally don't believe that every sin was put on Christ in the sense that the time Bill slapped his mom was worth a certain penalty and the time Phil grabbed a candy bar from the store had it's own specific amount of suffering penalty. But I do believe that, because of the worth of Christ and his suffering and death, the Father is satisfied that justice is done, wrath is propitiated, and forgiveness can indeed be offered in an almost outrageously generous way - but that the cost of this should be kept in mind.
The Bible says that we were bought as it were, with a price. We were "ransomed" but scripture does not specifically say to whom. Some of the church fathers thought it meant Satan. I think they were wrong, but I don't knock them because there does seem to be a sense in scripture that Satan had something on God so to speak, in that if God had directly gone after Satan in the beginning, God's own sense of justice would probably have caused us to be destroyed too. And for some reason, as C.S. Lewis says, he seems to love us. So I would say, and it's speculation, that in a sense the ransom was to God himself, and his sense of justice. In other words, to the extent we can understand it, he paid the price himself, using a plan devised by the Godhead, with the wrath and justice due us for our sin being laid on Jesus. I believe that as this happened God had in mind every sin that had been or would ever be committed by an elect person. As a side note, being all knowing, God had to have in mind the specific sins of the elect in a way that was different than the rest of humanity. You cannot get around this fact. I don't believe though, that the rest of humanity was structurally shut out in the sense that there is no sufficiency of atonement for them. But that is penal substitution, derived yes, but from a multitude of scriptures.