The only problem with your post is the suggestion that a combat system that would be in service to the story would suck. One thing has nothing to do with each other, because a tight combat system is compatible with any story.
So, most people don't want to delve this deep into the craft, because it "ruins" the experience. They start thinking about how things are made, rather than just enjoying them as an experience. So, fair warning.
Outside of things devoted to combat, like Kung Fu movies and old rpgs, when you see combat in entertainment, it is not actually about the physical struggle between the characters. Rather, it is about the personal conflict, with the fighting merely being an outwards expression of the personal conflict between them. That personal conflict is what gives the fighting weight. Modern moviemaking has, of course, thrown this idea out, along with so much else, and just dumps fighting in wherever there needs to be an action beat, and then uses whatever "cool" moves are currently popular without regard to character or theme. Which is why most fights these days are just kinda there, kinda ho-hum, even if they are technically impressive as fights.
And the reason for that lies in what things can elevate a story from the hum-drum to the good. Most rpgs have a long list of combat skills and some non-combat skills. And what all of these skills have in common is they are about interacting with the physical world of the story. Which is fine in a game that is itself about interacting with the physical world, such as an old rpg - ie, killing things and taking their stuff. But if the focus of the game is instead story, then all of these skills will only allow you to interact with the story at the most base of levels. Sure, the dev might put in a butterfly effect - you use your skills to save the princess, and the princess goes off and claims her throne and yadda yadda. But here, you did not interact with the story directly. You did not use your Galahad-purity to save the day, thus lending a higher meaning to your actions. You just used some skills.
And this fact flies in the very face of good storytelling. Even at the very basic, to have a good Tragedy, the tragedy should be caused by the main character's foibles, not something that just happens to some random dude because reasons. The main character's foibles are what gives the Tragedy meaning to the audience, and what makes it satisfying for them in the end, when the character dies.
In a story-based game, the Player should be interacting with the story at every level, not just the most base level. And the character sheet should not be a list pf physical and combat skills, it should be a list of things related to story and personality, since that is what the game purports to be about. Then, to bring all this that back to story and combat. Once story is the focus, once the goal is to tell a good story, combat naturally falls away in importance. Because first and foremost, in a story, the end of any conflict is decided by the story, not by the actions of the Player. The story tells you when and where characters will die, not dice rolls. The story tells you when combats will happen and how difficult they will be, not the character's stats and the Player's strategic actions. The story tells you whether you will win the game or not, not that gameplay.
And so, putting it all together, if the goal is to make a quality story with interactive stats, the best way to go would be to throw out physical stats completely. You make a choice at character generation regarding role, and that determines your fighting ability and style, and that ability and style never changes. Because the changing stats in the game are all based on story, not combat. As they should be in a game purportedly
about story. So, utilizing, for instance, Pendragon's system, with it's paired morales of things like Lust/Chaste on a 1-20 scale, with Lustful at one end of the spectrum at 1, and Chaste at the other, at 20. Then each religious Faith has, say, five favored traits, and if you have high marks in those traits, your faith grants you a bonus. Then the key is, these stats are how you interact with the game, not skills. For instance, your character encounters the Temptress, and your Lustfulness gets challenged by her. And you, as the Player, can choose to have your character attempt to resist the temptation, or succumb to it. And then, the character would roll for Lust, and based on their choice and the result, a story-based event would occur, with the character perhaps fighting and losing to his lust, or remaining chaste and pure, or being already lustful and just giving in. And in that way, your character would be telling the story himself through the actions of his personality, instead of the story just kind of being thrown at him in random blobs of exposition.