What I don't see anywhere here is reference to a hard-coded prep model of an in-game reality, where the location of the papers is pre-set by the GM and the PCs will eventually either find them or they won't. This would seem to suggest a fourth type of resolution, whether called "task resolution" or "puzzle solving" or whatever.
As noted, "high-myth" implies both high-prep and low-mutability in play. If there is a gorge, it's there because GM drew it on their map when they prepped their campaign.
On a broader scale, in the various scenarios you're proposing is there the possibility of an outcome where the PCs outright fail to find the papers at all, thus either shutting off that line of drama/story either temporarily or permanently or greatly diverting it?
So this is the problem that Baker's thoughts on high-myth and conventional approaches to resolution, and Harper's bottom diagram point to. If the goal of a scene is X, but resolution of the scene doesn't concretely resolve for X/not-X, then you get open-ended scenes. Where's the endpoint? Who is that up to and what are their compelling/constraining rules or rubrics for deciding?
I've mentioned that you get the same thing with "unlucky or error-prone players" in conflict-resolution. A string of misses leaves the scene open unless - like 4e skill challenges - the game procedure also tracks misses to close the scene (not all do.) Strings of poorly chosen and contradictory goals can close a scene without that scene contributing anything to resolving the overall situation. At least, not in any satisfactory way. You can see the virtue of a system that takes heed of interstitial resolutions while advancing inexorably toward closure, and thus are born skill challenges (4e), clocks (BitD), journeys (ToR), momentum (L5R), progress tracks (Ironsworn), and etc.
Example (I hope!):
Player: "I crack open the safe in hopes of finding the demonic papers the mayor told us about. Jory, keep watch at the door."
GM: "Ok." [invoke system's resolution method, to a 'fail' result] "Result: you open the safe but find nothing in it...and Jory, you hear footsteps rapidly approaching the door!"
Player: "Maybe that mayor ain't so honest as we thought he was - this is a trap!" (etc. etc. as the PCs try to escape)
So here the players never find the papers they wanted and worse, are driven away from further searching the place they'd been told to look. The story has to take another direction. Can this happen, in the sort of system you're talking about; and if it can't, how can that be justified?
Under conflict resolution, that can happen on a fail, as a hard move. It's a trap! Under so-called task resolution, it can happen on both fail and success, given high-myth. We can't crack the safe / we crack the safe but the papers are not inside. When I look at things folk do that I can't see the sense of, or that I disagree with, one question I ask myself is - from what angle does this make good sense? Where's the payoff for doing it this way?
To use an analogy (and I'm famously terrible at analogies) think of task resolution as the chisel in the hands of a sculptor addressing a block of marble. Each good stroke of the chisel (successful performance) brings the sculpture further into definition. At some point, the sculptor sees that their creative purpose is achieved, and they put down the chisel.
So with task resolution, if the player character performance - succeed or fail -
doesn't end the scene, then what will? 4e's approach is just to count successes and failures, and end the scene at the stipulated count. You can see why folk played it differently - some conflict resolution, some task resolution. It works either way. But the scene ends whether or not the fictional position at that point feels dramatically appropriate. Referring back to my analogy, we've given Michelangelo fifty chisel strokes - no more, no less - to create David....
Thus, another way is to care about setting and situation prep, and dramatic appropriateness. The right performances culminating in the right fictional-position. We talk about GM as author, sometimes without giving that characterisation any real meaning beyond "they get to decide things". But authors don't just decide things, they pursue a creative ideal. So with the sculptor, and so with the player character performances that together culminate in the right fictional-position.
In the end, it's more important to rehabilitate the construct than change the language. Resolving tasks for their own sake is absurd. Either they're resolved for the intents they express, or for the sake of their effect in shaping - sculpting - the fictional-position. Task resolution must be understood in a way that has explanatory power and utility to play.
Examples
High-myth + task-resolution (demonic papers are concealed in a Bible on the bookshelf)
Player: "I crack open the safe in hopes of finding the demonic papers the mayor told us about. Jory, keep watch at the door."
GM: "Ok." [invoke system's resolution method, to a either result] "Result: the safe's too tough to crack / you open the safe but find nothing in it... and [complication] Jory, you hear footsteps rapidly approaching the door!"
Player: "Maybe that mayor ain't so honest as we thought he was - this is a trap!" (etc. etc. as the PCs try to escape)
GM has a dramatically appropriate fictional-position in mind up-front, and character performances haven't reached it. It might be wondered, why should we care so much about what we had in mind up-front if something better emerges during play? On the other hand, what really is the motive for compromising if we don't find it satisfying? Play for enjoyment.
High-myth + conflict-resolution (demonic papers are concealed in a Bible on the bookshelf)
Player: "I crack open the safe in hopes of finding the demonic papers the mayor told us about. Jory, keep watch at the door."
GM: "Ok." [invoke system's resolution method, to a fail result] "Result: You crack open the safe [apparently successful performance] but find nothing in it [failed conflict]... and [complication] Jory, you hear footsteps rapidly approaching the door!"
Player: "Maybe that mayor ain't so honest as we thought he was - this is a trap!" (etc. etc. as the PCs try to escape)
The risks of conflict resolution are irrelevance of performance to result, and reaching. See Baker's comments on players wanting to go large with their goals, and talking them down. But what if a player says nope, it's sins absolved or nothing!?
High-myth + conflict-resolution (demonic papers are concealed in a Bible on the bookshelf)
Player: "I crack open the safe in hopes of finding the demonic papers the mayor told us about. Jory, keep watch at the door."
GM: "Ok." [invoke system's resolution method, to a success result] "Result: the safe's too tough to crack but as you are turning away you notice the spine of a bible sticking out a little further than other books on the shelf... the papers are tucked inside... and [complication] Jory, you hear footsteps rapidly approaching the door!"
Player: "Maybe that mayor ain't so honest as we thought he was - this is a trap!" (etc. etc. as the PCs try to escape)
Makes you wonder what the point of all that prep was, right? for conflict resolution. Would it really have mattered if GM had just narrated the papers being in the safe players were focusing on?
Low-no-myth + task-resolution (players are hunting for demonic papers but GM hasn't prepped their location)
Player: "I crack open the safe in hopes of finding the demonic papers the mayor told us about. Jory, keep watch at the door."
GM: "Ok." [invoke system's resolution method, to a success result] "Result: You open the safe and the demonic papers are there, rustling and crackling even though there's no air movement... and [complication] Jory, you hear footsteps rapidly approaching the door!"
Player: "Maybe that mayor ain't so honest as we thought he was - this is a trap!" (etc. etc. as the PCs try to escape)
Low myth gives GM greater freedom because they haven't decided in advance that one perfect shape they care about. Maybe it'd be like carving sympathetically in knotted wood. A shape emerges, but rather than being the exact figure you had in mind in advance, it's the figure that was contained in the wood itself.