So you discount John 10:11? May I ask why? Do you think perhaps that the giving of our Lord's life is something of a lesser order than the shedding of His blood?
"Behold, we are going up to Jerusalem, and the Son of Man will be betrayed to the chief priests and the scribes; and they will condemn Him to death and deliver Him to the Gentiles; and they will mock Him, and scourge Him, and spit on Him and kill Him. And on the third day He will rise" (Mark 10:33-34).
Why do you think that the Lord Jesus had to go through such a terrible ordeal? If all He had to do was shed His blood, He need not even have died; He could have come down to earth for a day, given a pint of blood for the world and gone back to heaven!
But the life is in the blood (Leviticus 17:11). The many references to the Lord Jesus shedding His blood are a synechdoche; the part stands for the whole. The blood stands for the whole of His atonement: His living the life that we could not live-- the life of absolute righteousness and obedience to the will of the Father-- and taking the punishment that we deserve to suffer-- the punishment of pain and separation from God.