Jesus is the mediator of the new covenant between Jehovah God and the anointed Christians numbering 144,000. No argument there. The rest are not part of that covenant but we benefit from it. I don't see the problem with that.
What is an alliance if it is not a promise between two parties? The answer you provided is the official teaching and you will note that they don't say it often cause if you stop and think about it, its bunkers.
You are not part of the alliance, but you are expected to devote yourself to Jehovah at least 20 hours a week (personal study, family study, meetings, field service). That's a lot of time to not be part of any official alliance.
Of course, this will not trouble everyone, but if you incorporate it often enough in your talks, prayers, comments, discussions, some will start to stumble on it. I'll admit that this is a challenge as repeating it too often could even sound apostate, but there must be a way to bring it forth every now and then.
One approach that easily works are biblical quizzes in the field ministry, between calls and doors. You know... how old was methuselah? What were the names of the three Hebrews who didn't bow down to the idole? What are the alliances mention in the bible and between who? Trick question: Are we part of any alliance? What are the two pivotal dates on which our chronology relies?