If the client could recognize the selected deck trying to join as having either zero, no more than three, or greater than 3 game changers to pair up with the custom match being selected as bracket 2 or lower, bracket 3, or bracket 4 or higher that would likely help a lot of higher bracket decks pairing down while also still letting lower bracket decks pair up if desired.
A bonus to help the cEDH players at bracket 5 not get non-cEDH decks joining their rooms would be to have a toggle on decks that manually mark them as being bracket 5 and only decks marked as being bracket 5 could join bracket 5 rooms. Possible mock up pictured.