Your axiom is that a FAF game must always be balanced so that everyone has a 50% chance of winning rather than being meritocratic and rewarding improvement in skill. It doesn't matter how good I am, I will always have the exact same probability of succeeding.
You basically want to turn the game into literal rock-paper-scissors. And that's giving you the benefit of the doubt and assuming you have actually found the perfect values between ratings to reach your intended goal. This is not a replacement for trueskill, it is literally anathema to trueskill. This is a mod for the game, not a new rating system.