This is what the Bible says about Jesus as mediator: “Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance” -- Heb. 9:15.
This is not the work of reconciliation. This is an organizational covenant, just as the old [Mosaic] covenant was organizational. The question is, then, are the Great Crowd under the new covenant, or is there a separate "Israel of God," limited in number? If we answer as Jehovah's Witnesses do, that only a limited number are in the New Covenant, then all else is not. Jesus did not negotiate a covenant with them. If we answer as some others do, that every Christian is part of the new covenant, then the Great Crowd has Jesus as its mediator.
However we answer, an organizing covenant is not the work of reconciliation. That's Jesus' role as atonement sacrifice, and in that role, John the Apostle calls him the propitiatory sacrifice for all. The two terms are distinct both in English and in Greek. Purposely confusing them, as some are doing here, persuades only the choir.
Being exact and accurate in our criticism matters.