We've already refuted the blood-atonement doctrine earlier, in many places. Edgar Jones
here has an interesting thesis showing Paul to be the originator of the 'Eucharist' with its blood-atonement emphasis, while this 'ceremony' was later incorporated (written) into the gospels.
The UB presents Jesus as incorporating this ritual as a 'remembrance supper', a physical and spiritual sharing of God's Life in the heavenly kingdom, we living that kingdom here in the physical world. The emblems of 'water/wine' and 'bread' are symbolic of the life substance, so these are shared among the company of God. This can surely be acted out without a concept of 'vicarious sacrifice', for it is the outpouring of God's life thru Jesus in the very fact that he 'bestowed' himself to us in the flesh and ministered, and poured out the Spirit of truth after his resurrection. These are all heralded in the papers as part of the good news.
It could be that Paul knew of a tradition of Jesus 'rembrance meal', and then invested the cup of wine with being 'blood', in some kind of atoning/redeemer manner, in his own gospel-teaching,
putting in that added element, then this was later infused into the gospel records. According to the papers, there was this 'memorial observance', but its tokens
do not include the concept of 'blood-atonement' for sins,
but life-nourishment of the Spirit. In any case, it is the Spirit that gives life, whether you believe in a blood-sacrifice or not (again its principle can be rejected). The key here is that Jesus gave his life as a love-offering, and was faithful to the end to the Father's will, showing us how to live, modelling the perfect 'religion' that we are to adopt. The UB emphasizes the 'religion of Jesus', HOW he lived, as our model to emulate, living the life of faith.
pj