In regards to your preference for the out-of-combat mechanics of 4E over the 5E playtest, I honestly don't see a great deal of difference between the two. I wouldn't be surprised if we see an optional Skill Challenge system in the DMG. But generally speaking, a check is a check in either edition.
My main interest is in the principle by which DCs are set. The "objective" approach has consequences that are different from the "level-appropriate" approach.
I think you may be surprised by how much discussion and how many options there are around check resolution in the core books. Mearls has talked about optionally making use of storygame mechanics (like "fail forward", for example), and I'd expect some discussion of these kinds of options in the DMG. D&D will never be Burning Wheel (a game which I adore, by the way), but I expect that it won't be hard to bring a few rules in to strongly encourage story-making play.
It would be good to be surprised! I don't have a strong sense at the moment, except that there is continuing very strong and widespread hostility to discussions of "saying yes" and "fail forward" approaches in the 4e DMGs.
On the issue of the tiers of play indicating appropriate actions for the players to take: this is not really something I've given much thought to, because I'm not really a fan of "superhero" D&D - I prefer a grittier game, which 5E seems to suit better.
I think this is also part of how Burning Wheel is able to accommodate "objective" DCs - it is prepared to be gritty (certainly grittier than 4e).
But BW's also prepared to have a lot of auto-fail-without-artha, which means that - in combination with its
very bounded accuracy and its shade rules - it can use a rather narrow band of DCs to range from trivial to superheroic difficulties. D&D's d20, however - in combination with the absence of any artha, HeroWars/Quests-style "bumps", etc - means that I think D&D has a harder time achieving the same outcome, of things being (i) accessible to low level PCs in extremis but (ii) generally impossible for low level PCs while (iii) feasible for high level PCs.
Hence I think 5e will tend perhaps to be even grittier than BW. My personal reason for preferring 4e to gritty D&D is that higher-level spell-users get to be non-gritty (via their packaged mechanical elements) while the same level non-spell-users are not able to use improv around the skill rules to achieve the same degree of non-grittiness.
How do you rule on characters trying to do something different with their powers, alter them in some small way which would seem logical that they could do given the given narrative of the power. Do you just allow it? Have them roll to alter it? Perhaps cost a surge?
It depends on context and intuitions about mechanical balance. For instance, using Thunderwave to blow a demon through an ordinary urban shutter in a small upstairs room required an Arcana check. Sometimes I exact damage or a surge as a "tax" for the power-up. Sometimes everyone at the table just thinks something is fun or make sense and so it happens (like being able to make an Acrobatics check to "Gandalf" the Aspect of Vecna).
You challenge the group based on character-levels whereas the challenges I set are also affected by in-game fiction.
My quibble with this would be that I also challenge via ingame fiction - eg the whole confrontation with Vecna is based around ingame fiction, of killing angels of Vecna and taking the Eye from them and then implanting it in the imp to combine (i) power-up with (ii) blocking the channel between the imp and its spymaster.
But if you mean "I establish the mechanical feature of the challenges by reference to character levels", then yes. For instance, the players in my game know that they can't make a task mechanically easier by waiting a few levels before undertaking it, as I will just level up the numbers in response. To make it easier they have to change the fiction.
These two things can also interact. For instance, when the PCs become paragon tier, it is easier for them to fight hobgoblins. Hence, encounters with hobgoblins mechanically are framed as encounters with hobgoblin phalanxes (Huge or Gargantuan swarms) rather than as encounters with single hobgoblins. This is a change in the fiction (they're now paragon tier) which affects the way I frame the fictional character of the challenges (you're not fighting 4 hobgoblins, you're fighting a phalanx of one hundred or more hobgoblins!). The encounter is not mechanically any easier (they face an encounter with level-relevant swarms put together to serve the right pacing and similar needs as per the DMG guidelines mediated through my own familiarity with the system and my group). But the fictional stakes and consequences of victory are very different (defeating the hobgoblin phalanxes can save a town, and hence change the PCs' relationship to the world quite differently from when, at 3rd level, they beat up half-a-dozen hobgoblins and stole their armour).
The purest example of this approach to the fiction-mechanics interface I know of is Robin Laws' HeroQuest revised. But 4e lends itself (and, in my estimation, was deliberately designed so as to lend itself) to the same sort of approach.
