I love your impecable logic in this discussion. One thing you left out though: God cannot simply visit justice on Himself in our place, or else the incarnation, the coming of God the Son in human flesh, would be unnecessary. Only God was capable of handling our punishment, but only a human had the right to take on that punishment. An angel or even God, before the birth of Jesus, could not, by His just paradigm, take away sin (permanently) only someone who was uniquely human AND God(Jesus Christ) was capable of our sacrifice.
A perfect and sinless man, who also had to be God. As St. Anselm put it, the God-Man.