So did they show you a scripture that said Jesus was the mediator for everyone, not just the anointed? The WTS teaches that Jesus corresponds to Moses as the mediator and that Moses mediated the law covenant between God and the Israelites.
The WTS eaches that Jesus is the Greater Moses who mediates the New Covenant between God and spiritual Israelies, which the WTS defines as being only JWs who have the heavenly hope. All other JWs are not part of the New Covenant and thus Jesus is not their mediator.
The confusion that most JWs have is that 1 Timothy 2:5 talks about Jesus being a mediator between God and men in reference to prayer. The WTS does teach that all people just pray through Christ as their "mediator."
Most JWs get disturbed when either a non-JW or a JW points out that Jesus does not mediate for the JWs who do not go to heaven.
If you can get a JW to get past their cognitive dissonance, they might admit that this is what is the official WTS doctrine. Most live in la-la land and shut their ears to any other explanation.
The best thing to do is put the burder of proof on them. If they say Jesus is the mediator of everyone, they should be able to show a scripture or at least a quote from some WT publication.
You have shown them excellent quotes...but I have found that JWs have thick skulls when it comes to understanding this.
*** w03 2/15 p. 22 What Does the Lord’s Evening Meal Mean to You? ***Anointed Christians are certain of their heavenly hope, of their having been taken into the new covenant. Jesus mentioned it when he instituted the Memorial and said: "This cup means the new covenant by virtue of my blood, which is to be poured out in your behalf." (Luke 22:20) The parties to the new covenant are God and anointed ones. (Jeremiah 31:31-34; Hebrews 12:22-24) Jesus is the mediator. Made operative by Christ’s shed blood, the new covenant took out not only from the Jews but also from the nations a people for Jehovah’s name and made them part of Abraham’s "seed." (Galatians 3:26-29; Acts 15:14) This "everlasting covenant" provides for all spiritual Israelites to be resurrected to immortal life in heaven.—Hebrews 13:20.