It makes sense to me, and I thank you a lot for this thorough explanation,..
As I understand it, I should pay more attention to my FOV, it does change across some of my games.
There is an autoFOV calculation feature, and I will use this to automatically calculate all my games so that the HFOV is 103°. Most of my games go above 103, and I'm not really willing to go much lower than 100 so I think it's a good baseline.
I'm not sure how much of an impact aiming really affects the sensitivity, but in most of the games I play I can't either tweak it so that it feels the same or it already does that on its own.
I have come to understand more about horizontal monitor distance and scaling and keeping everything at a 100% should do exactly as I want.
Using this method whilst keeping the same FOV across my games I can tell that sensitivity feels entirely the same for all these 3 games: Hunt Showdown, Overwatch, and R6 Siege. I haven't tried COD yet, but if there was any problematic game, it was usually this one for me, I'd have to download it again to test.
As for the vertical monitor distance, without understanding much of what it does, I can already say that if there really is no way,... That your method might be the next best thing.
I guess I'll be testing out when I get to game and report back!