We can see that Paul is addressing the issue of prayer in these verses, not Jesus acting as a mediator of the new covenant. There was no “great crowd” then, just Christians and non-Christians, and that Jesus was the only channel through which prayer could be offered to God by humans, not just the “anointed.”
How come I never noticed that before? It's as clear as the nose on my face. Paul's context is prayer, not the new covenant. That makes sense because he is also speaking about the benefit of Jesus' mediation for everybody, or "all sorts of men," "for all."
This idea that Jesus is the mediator for only the 144,000 never did make a lot of sense. Maybe the 144,000 are the only ones taken into the new covenant. But as you show, that is not even the focus of Paul's words about Jesus being the "one mediator between God and men." It is prayer.
Thanks, Blondie, for turning on the light!