Where the bible is concerned, there are always multiple interpretations available. The one you've laid out here is valid -- but not the only valid one.
In the parable of the leaven, Jesus says that the Kingdom of God is like leaven that a woman mixed in with the dough, until the whole lump was leavened. In that time, leaven wasn't yeast, like we have today. It was toxic. So, the Kingdom is like something dirty being mixed in with the dough, until the whole lump is dirty. The point: We cannot become clean enough to reconcile ourselves to God, so God becomes dirty -- thoroughly mixing in with the lump of humanity. Through God's act of becoming one of us, to the point of even dying like the very least of us (a dirty, toxic criminal), God reconciles humanity to God's self. It, therefore, is the act of Jesus becoming fully human, fully dirty, fully vulnerable, that reconciles humanity.
The death is necessary as a precursor to resurrection. Jesus had to be "laid down" in death, in order to be able to "get up." We are not saved because our sin is washed away by divine blood. We are saved because, since God became fully human (by becoming fully mortal), we, as human beings, participate in his "getting up." It (as you surmise) is a rather new concept that comes partly from the Greek notion of an afterlife, which wasn't fully present in the Judaic religious scheme.