Using the name in water baptism is where the blood is applied - and you obtain forgiveness of your sins. It is not the water itself. It is thru the power of the name. But that is where your sins are washed away. See Acts 22:16 - Where Paul was told to arise and be baptized and wash away your sins. Calling on (or you could say invoking) the name.
I am not sure what a technical definition of a Unitarian is. I am not claiming to be one. I just know I believe in one God and not a Trinity. The one God that I believe in took on a fleshly body, and shed his blood for our sins.
Your last point doesn't really make sense to me. Because what essentially happened, is the one and only God wrapped himself in flesh, and shed his blood for us. Then he raised the body up a glorified eternal spiritual body, and ascended and took the throne.
If the power of water baptism comes from using the name of Christ, then why place such emphasis on a ritual using water. All you have done is confirm that water is an outward symbol. It is not water that washes away sin; it's the Holy Spirit. But for the Holy Spirit to come there must be repentance and belief in Jesus Christ. That's where the name is used.
I also believe in one God. So, rather than argue about the theologian terms, it's better to prove a point using scripture alone. That's why l ask those that claim to believe in one God whether they believe Jesus Christ is worthy of our service. It saves having to talk theology.
The final point is important because there has to be a clear distinction between what is 'man' and what is 'God'. Numbers tells us that God is not a man. God tells us that He is Spirit. Paul tells us that flesh and blood cannot inherit the kingdom of God. So, what are we to think about the soul? Is it of the Spirit, or is it of the flesh?
In the story of Jonah, which Jesus refers to, Jonah descends into the grave (sheol), meaning that he dies. Thereafter, his soul communicates and prays to God. When he is finally spewed up on dry land, his soul is back in a living body.
Jesus' soul descended into the grave at death. He is said to have made himself known to all souls that had died up until that moment. His soul was in the grave for three days and nights before being raised in a new incorruptible body. It was God's Spirit that raised the soul of Jesus from the grave and gave it an incorruptible body.
At the ascension, Jesus' body and soul, now united with the Holy Spirit, ascended to heaven.
If Jesus pre-existed in heaven with God, which part pre-existed? Did the soul of Jesus pre-exist in God, or was the soul a part of the body born to Mary? If the soul did pre-exist, why is God described as Spirit, and not as Spirit and Soul?