Well, just to put my own experience out there I've tried a couple of things to bring a little PbtA to my 5E table. The low hanging fruit, so to speak, is to frame narrative consequences for failed rolls and introduce complications like that. This requires two things. First, you need the players on board (obviously) and, second, you need to be pretty moderate in calling for rolls. By that I mean I only call for rolls when it really matters, maybe a little less often that some DMs, but I tend to be pretty hard on DCs and my players know that the DC represents the situation and task, not just the task. So depending on the fiction, a failed roll might be success with consequences if the better part of the DC were situational rather than strictly task related, or just failure if its the task itself that is most of the DC. I didn't find this to be a huge cognitive load, but it was with players with PbtA and related experience so they knew what the goal looked like. I think it would be a steeper learning curve for D&D-only type players.
I can absolutely follow your posts and understand your reasoning. All I can say in response is that I think you're getting close to treating the gold standard of a system like BW or AW as the floor!
In AD&D played vanilla narrativist, it's closer to AW than BW in the following sense: there's less of a sense of "scene stakes" and more of a sense of the "local" (for lack of a better word) stakes of a particular check. (This also fits with there being nothing like a skill challenge.)
But the GM can set a difficulty for checks, and honour success. And there can be a practice of allowing retries on a miss of (say) 4 or less (on d20), with the cost of a retry being some sort of fictional escalation like the passage of time or having to increase the offer to a NPC or similar.
That's a bit different from the approach that @Campbell has described. It can be done in AD&D. I can see that 5e has more moving parts. It might work better in 5e for a rogue, a fighter and a warlock than (say) a paladin and two full casters.
I think it works mechanically, there is simply, in AD&D at least, nothing to 'latch on to' in the character, aside from class and race, to drive the engagement thing. DW has bonds for example, or BW has beliefs. So, the question is still kind of what exactly are the checks accomplishing? In a DW game the player makes some choice/answers a question then the GM presents a 'move' and there's a check, and either the player's intent is realized or not (usually with some caveat). So, lets assume you played AD&D in a scene-framed DW-esque fashion, then these checks you speak of (which are basically a de-novo mechanism, though later 1e and then 2e do have some limited generalized check mechanics) can 'work the plot' like they do in DW (IE they reflect plot randomization, not "what is the probability Joe the Dwarf can do X in situation Y"). However, you do run into some flies in the ointment, like thief abilities and such, and the general plethora of types of dice rolls. You COULD simply reform such mechanics, or live with it. So, its a bit of a mixed bag.
Now when you go to 5e, then you do have some 'personality' stuff that can be officially added to a PC, and a background, which is reasonably meaty (easy enough to flesh out, they are fairly suggestive). So, I guess it isn't HARDER, you can employ fixed DCs that just scale a bit with level, so 90% of all checks fall within a couple points of nominal chances, and then employ "and if you miss by only 4..." or something. Its not quite DW!
I would say you are subverting AD&D (1e certainly) MORE because you will surely only use a lot of the mechanics more to bring something like 'fronts' to life. So, for example, wandering monsters are not likely to be random! Maps full of rooms and whatnot are going to need 'holes in them', etc. and obviously the central 'test the player' paradigm is largely subverted (though I am reminded of @Manbearcat telling us that the various ways you get bonuses in DW are in fact a mechanism for injecting skilled play). 5e/2e are subverted a bit less, since they already kind of gave up on those skilled play concepts anyway, largely. 5e gets a bit weird in terms of different pressures on the PCs due to resources. OTOH DW doesn't especially allocate things symmetrically in that sense either, each resource is either a potential trade-off (do I forget my spell or attract unwanted attention) or a 'screw' to turn via a 'soft move'. 5e at least does offer full casters the old "how many slots do I really want to burn to get this done?" which could be levered by the GM in a few ways. Its a bit trickier to put pressure on, say, a Battlemaster in that sense, though hit points are always the classic standby.
You just definitely, in all cases, need to forget everything you ever learned about traditional GMing of these games! If I were to try to run 1e this way it would be hard not to fall back into old habits, and the fact that the game has all the levers to cater to those won't help, lol.
So, lets assume you played AD&D in a scene-framed DW-esque fashion, then these checks you speak of (which are basically a de-novo mechanism, though later 1e and then 2e do have some limited generalized check mechanics) can 'work the plot' like they do in DW (IE they reflect plot randomization, not "what is the probability Joe the Dwarf can do X in situation Y"). However, you do run into some flies in the ointment, like thief abilities and such, and the general plethora of types of dice rolls. You COULD simply reform such mechanics, or live with it.
Yeah, and of course its all subject to heavy interpretation as to when it is even appropriate to ask for things like Climb Walls checks. If you take Gary literally, at least the PHB, then the only time the checks even matter is if it is a SHEER wall, one that wouldn't even normally be climbable (I guess the assumption is any adventurer whatsoever will automatically scale anything easier, though that goes mostly unsaid). Of course the DMG seems to muddy those waters somewhat... In any case, it is certainly POSSIBLE, though the result seems like it won't resemble your Mom's D&D very much.... (yes, my Mom has played a pretty respectable amount of D&D! LOL, though she seems to have 'retired' of late from what I hear).