Does this help?
Somewhat, but feel free to take a crack at the wrestling hypothetical I posted above. :)
I get the whole what's-it-matter-to-the-story thing, but there's a bit of an inconsistency here that I'm having trouble negotiating. On one hand, I've read plenty about how this isn't a sim system. But on the other hand, it actually is. The aspects you're testing aren't your character's propensity for trouble, bad luck, drama magnetism, etc. It's Strength, Dexterity, Charisma, etc. The character breaks down into some pretty sim elements. So, the character with Strength +3 is stronger than the character with Strength -1. When I'm doing a Strength test, it's because the task at hand requires Strength. Nevermind comparing wrestling a dragon to wrestling a puppy. These are both pretty common sense situations. But, if I'm wrestling a GM char that's a little stronger than myself vs. one that is a little weaker, according to the RAW(:D), I have the same odds against both. It's a GM char, so there's no opposed check. My roll doesn't get a modifier. You might have this multifaceted narrative potential in front of you, but the player only has a single port of entry, their own simulated and static measure of general competence.
The multiple check thing is a bad idea, not because of the narrative constraints, but because of the math. For the sake of simple mathematics, let's say we have a character who is average at everything that needs to be tested for the check and has no modifiers from anything else. For a single check, that character has a 58% chance of success. If it's a little complicated and they need a follow up check, then their odds drop to 34%, add a third check and we're down to 20%. If you did this with flat modifiers for each difficulty, your odds would go 58%, 42%, and 28%, respectively. It's less harsh and gives you more play to account for the external environment with which the characters interact.
I think the idea of the narratively-driven follow up checks is clever, especially if you have to tap into different moves to pull off a combo. But the math really bites you in the ass. There's actually a pretty easy fix for this. Add in a "combo bonus". All these skills working in synergy give you +1 to your follow up checks until the larger task is done. So average (+0) for the first check, and +1 for checks 2, 3, and so on. There your odds go 58%, 42%, and 30%. You're actually getting pretty close to the mechanical effect of the flat modifier, but you're using the multi-check narrative approach. The only odd thing about it is that your narrative approach takes three times the dice rolling as just giving someone the -2 to the first roll. And, you're still modifying rolls. So, really, I haven't accomplished anything here. :P
But in the abstract, the question you should always be asking yourself when structuring these situations is "what is this roll accomplishing in the story?"
I ask (and usually answer) that question all the time. But I'm also asking, "What does this roll say about the world in which my character exists?" Every dice roll isn't just a beat in the story. It's also the in-game universe telling you, "I know what you want, but this is what you are going to get, because that's the way the world works."