Thanks for your explanation but I have a different soteriology and use scripture to back it up, this one for starters:The pre-fall Adam did not bear the sins of the world nor intercede for the sins of the world, I don't think there is supposed to be that direct a comparison. The comparisons made are "as in Adam all die/sin" so all those in Christ will "reign in life/be glorified."
If Jesus is taking the penalty of sin—however you specifically want to delineate that—the method used was mystical union with the sinner, which is why we are crucified with Christ, one spirit with Christ, and the body of Christ; which necessarily associates him with sin.
Christ became the curse of the law, he who knew no sin was made sin; if he did not really and truly carry our sin, but in name only, I think it would have actually been a breach of justice; and in that union with us he mediates with all humankind, even his own humanity.
I don't think it need be deduced that the life of Jesus had a personal sin or imperfection that needed atonement by these above facts, and Jesus did not die for his own sins; but by becoming the sin offering he was necessarily in union with sinful humanity.
Romans 5:18 So then as through one trespass the judgment came unto all men to condemnation; even so through one act of righteousness the free gift came unto all men to justification of life. (ASV)