Campbell
Relaxed Intensity
Again, this is all cool. I've played only a couple of the games you mentioned, but there are also many I have not. Over the years, I have played enough games to be exposed to a lot of different game mechanics that help with the game structure. I dig that stuff, even though I don't often think it is necessary.
Now, given that this is a 5E forum....do you think that 5E is incapable of achieving the kind of play you like? It's conspicuously not in your list. Do you think that absent such narrative mechanics in 5E, that DM Judgment can substitute?
You could get there fairly easy, although B/X or BECMI would be better fits. You would have to develop your exact Agenda and Principles to fit what the game uniquely offers and the exact sort of narrative you are after. Inspiration in its current state would have to go - it cuts against our interests in the same way that Fate Aspects do. It reinforces playing to who our characters are right now instead of making who they are a question answered through play. I would also scrap the current experience system and replace it with something more strongly tied to the sort of play I'm going for. A better rewards system is not strictly necessary for this sort of play, but the current reward structure is also counterproductive to our interests. I would probably also alter rest cycles in the same way I did when I ran 4e. Not insignificant hacks, but ones that don't really touch core systems that much. You can stop at just the principles, but there are some counter productive procedures I would not be able to help myself with.
Honestly if I were going to run 5e it would most likely be in a West Marches style. Create a map with blanks in it, have a larger group of players create characters, and have them coordinate what they want to do. Then prep exactly that material using guidance from B/X. Either that or run Sine Nomine's Red Tide sandbox setting or utilize some Red Box Vancouver modules - not adventures, actual modules.