I really dont see that 4e does not rely on the adventuring day. Everyone has Daily abilities, they all get a certain number of Healing surges per day with Action points that reset every day and items that also have Daily abilities. At high levels you get abiltiies like: "Once per day, when you die....". 4e is full of the normal DnD resources that need to be carefully hoarded and preserved. It kind of detracts from your main points to be honest.
But 4e is MUCH less a per-day gated game, and much more a per-encounter gated one than other editions of D&D. 'classic D&D' doesn't really have per-encounter resources at all. The main party resource, spells, are always per-day, as are hit points (essentially). I can't think of a good example of a per-encounter resource in AD&D at all, beyond maybe "thieves can only backstab once per encounter", but even that's not a hard rule, just an expected fictional limitation.
In 4e you can certainly continue to operate, even with many resources largely depleted. You get your encounter powers back, you have milestones which allow recouping of APs, and many item powers/properties are usable on either a continuous, at-will, or encounter basis. Its true, HS puts a cap on your day, eventually, but the limit is generally high enough that its more a question of management vs continuing until its expended.
If the DM is presenting or "framing" a room in a Gygaxian dungeon, and I must admit that some of those rooms can be very interesting indeed, how is that not meeting your first premise?
And then if the Players engage with that scenario then that must meet your second requirement as well.
Sorry I am still having trouble differentiating exactly what you mean.
Scene framing in Story Now is a process of reacting to player cues to produce a situation which challenges their character's beliefs/interests/genre-based questions. Gygaxian dungeon encounters are puzzle/challenge elements which are, by intention, unrelated to player/character choices, which are supposed to be made as part of a 'game of skill' intended to allow the player to showcase his expertise in overcoming the GM's diabolical schemes and monsters. One HUGE difference is that, by definition, dungeon encounters are set-piece things created ahead of time, while Story Now encounters are ideally created on the fly in a sort of feedback loop with the players. Obviously neither of these ideals is usually fully realized, but they exist.