I think stats are cool as long as they all serve a purpose at some point or another, unlike most of cogs flavor stats, and their flavor choices that also dont mean anything.
If the thing in question is going to offer multiple sets of consequences of varying degrees based off a stat, I could get behind stats. Maybe even if they can help drive the story forward in some way or serve as a way for the protagonist to solve various problems based off their skills or fail horribly for lacking the skill, or fail more or less horribly depending on the skill level. Which is one work around to consider.
So do you throw the character into social situations where they cant use their intimidation or strength stat and are forced to improve social stats, or let them awkwardly blunder through threatening everybody. Honestly the first sounds like it could tick the struggle and satisfaction part of someones brain. And you have a more fleshed out and well rounded character for it, perhaps even if they fail they have some minor success in the exchange and get a little stat boost because of it.
Usually stats takes the focus off the story and the importance of making the right choice. "Hey, it doesnt matter if I make a blunder in my choices because I can just muscle or charisma my way through it." So having a way to reconcile the two or fix that would be dope.
It sort of takes all the heart out of the characters struggle and upholding their ideals on a narrative level when done poorly. I think games that realize this tend not to get too wrapped up trying to take the plot too seriously and let people enjoy it for the number crunching thing it is, are generally the most successful storygames with stats. They sort of remove the chances for serious bulnders and are played for the funsies rather than emotional involvement.
And usually the goal of the game is to slay the big bad and take the treasure trove which will increase in game monies because its all about the numbers. Even though there isnt really much tension or suspense.
Otherwise failing to blend them would take the tension out of a scene, knowing you can get through it simply because the numbers are up. So thats something else that would require some kind of creativity to successfully merge.
However, if it was done well then it could actually be really satisfying. A character with heart and personality, and a story with scope and ambition that also works well with being an rpg.
Big narrative stories like Eternal focus more on the aspects that make a character memoriable in ways simply getting bigger numbers cant. If Eternal did go the route of using stats, for that particular style of storygame it would cheapen the experience (or perhaps not, I feel like End could also merge them well if he was inclined to use stats).
Yeah really the issue I am beginning to think isnt even with stats but the fact the majority of people that try to blend it all together fail because they put no effort and thought into it, and at a place like cog they are often rewarded and praised for their bland work.
Normally I would be tempted to say it should really just be either or when it comes to storygames (stats or no stats). I feel like you have a pretty good idea worked out for how to blend narrative and story with numbers together, having experience with both things.
I think as long as you make the choices AND the stats matter in a convincing way it should be good. Honestly its probably easier than it would seem. The only real difference being that it takes some effort to do, which not a lot of cog authors seem willing to do.
Anyways I am confident you would be willing to put in the effort and thought to make it all work and I cant wait to read your epic when its done.
Im not sure if Ive actually answered the question or not but to boil it down it all comes to the stats mattering, having a visible effect, and flowing seamlessly into the story.
Anyways, good luck on the epic and have fun with it.