I think I've hit on why the WTS love to downplay Christ's role as mediator. It's not just so that they can have their two classes of Christians. They have to downplay this aspect of Christ because it throws up the issue of his divinity.
Who is Christ mediating for?
Two parties; men and God. Therefore two parties need to have representation. And they do have representation; Jesus Christ. There isn't mediation from both sides, a mediator for men and a mediator for God. It's all taken care of by one mediator, Christ.
How could the mediation process work if Christ wasn't fully man and fully God?
Because Christ was fully man and fully God he alone is qualified to represent both parties fully and to mediate for them, creating peace. How could someone who was just a man mediate for God? And how could an angel mediate for God? How could Jesus mediate for man if he wasn't fully a man?
No wonder JWs hardly ever talk about Christ as their mediator. He not only isn't their mediator but according to their theology it's impossible for him to be any sort of successful mediator between God and men.