First I appreciate the effort to try and summarize the ideas nicely
From what I’ve read and understand, there’s no reason to expect the overall to be the average (in any sense) of the other ratings. They’re all separately calculated.
Also there’s more than just one number changing each game. If you play a blitz 9x9 game, your overall, blitz, 9x9, 9x9 blitz should all change with that game (if I understand correctly).
I tried to come with an analogy with a much simpler rating system than ELO or Glicko but still trying to capture some of the points you highlighted
the analogy being here for example Overall rank calculation - #10 by shinuito
Again feel free to pick apart that analogy. I don’t expect it to be perfect, I just wanted to imagine a system whereby your ranks vary and the overall isn’t necessarily an average of the others. Also that one could have your overall rank higher than any of the others (as can happen both in that example and on OGS with glicko - what kind of average does that!)