No problem! It's an awesome idea for a hack, after all.
I'm totally with you on those stories being something that need to be told through the fiction. But that doesn't mean they can't have mechanical implications, right?
They should do steps instead of resolving the whole thing, though. That is to say, mechanical implications that carve up the thing into little bits, like going aggro, seize by force, acting under fire and read a sitch carve up a violent encounter, as opposed to mechanical implications like the Hardholder's Wealth, which sums up a complicated process.
Now the following are ilde thoughts based on fairly recent play experience, so they're not reliable in any way. They seem to be relevant, though, so I'll share them.
So okay! In a game, you start with a capable protagonist, the best man for the job. Which is not to say they'll succeed, but rather that if anyone is going to succeed, it's them. So, like, if there's a Bastion in play, whether or the 'hood is saved from the sharks swirling around it depends on how good the Bastian does (and not some random NPC).
To begin with, the character faces fairly simple problems - Walter White wants money, he makes drugs and finds a guy who helps him sell them. All of this he accomplishes easily.
But things escalate - Walter White finds he needs to kill a drug dealer and then remove his body, only to eventually have an even meaner drug lord take the killed guy's place.
That's where advancement comes in. It allows a kind of bump-around - we find a capable character in a situation he is no longer capable in; he gets knocked around a bit; he becomes better and tries a new approach to the problem.
So character advancement is there to make sure that characters can become capable as the situation escalates. Eventually, it can be expected that it will escalate to the setting-level questions of the game (what is the maelstrom and how do we deal with it? Can a person thrive in the post-apocalypse? Can a person escape the 'hood? Can a person live a good life in the 'hood?).
So how you advance is the story of how you become capable to deal with the setting-level problems. In AW, you do that by being cool, hard, weird, and etc. In the 'hood, I imagine, you become capable of dealing with setting-level problems not because of skill or ability, but because you deal with your money and your name succesfully - you get more money, you protect what you have, you spend your excess, you deal with a shortage.
Now, since I believe all of the above, I think that your game will be awesome at looking how characters deal with problems as they arise... But that it may or may not (that is to say, not depending on the game as written) address any of the big questions of the settings. I'll have a game where I'll get to see how the Blur tricks people, gets into trouble for it, and then tricks them again to solve his problems. But it'll be harder to see if the Blur ever gets enough cash to set up a life that isn't a lie, or one that is a more beautiful lie than it is now.
To get that stuff, there need to be real, rule-supported ties between dealing with money in all of the ways possible and advancement and, through it, various game bits.
Any of this make sense to you?