The solution, in my opinion, is to take the DC by Level chart as a guide and extrapolate a bunch of static DCs for common actions that can be prepared in advance. This way, the DM has a strong resource to rest their rulings on and won't be tempted to get all quantum ogre-y.
The other advantage of such a resource would be that you could make it open to the players. This would encourage them to try more interesting maneuvers because they have a whole bunch of suggestions, and they even know exactly what their chances are of success.
But writing up so many DCs is a pretty mammoth task! If Wizards of the Coast were cooler then they probably could have done it for me; it certainly would have been a better use of their time than, say, the Bladesinger. But still, I'm going to give it a shot, going through the skill list alphabetically.
First of all, some general modifiers:
Afflicted by negative condition (dazed, slowed, etc.): +5
Under pressure (being attacked, threatened by traps, etc.): +5
(Note: It is up to the DM to decide whether modifiers apply on a case-by-case basis. For example, being immobilized by vines would not result in a penalty to a knowledge check, but being dazed certainly might.)
I think stacking on extra difficulty modifiers could be a great way to make the players feel more badass. i.e. "I'm level 4, I can climb this rock wall no sweat." "Yeah, well I'm level 12. I can climb this rock wall in torrential rain... while I'm on fire."
And here are all the most common actions I could think of for the first skill, Acrobatics:
Perform acrobatic stunt (swing, somersault, slide, tumble, etc.): 15
Failure: You fall prone.
Escape from a grab: DC = grabber’s Reflex save
Escape from restraints (rope): 20
Escape from restraints (manacles): 30
Escape from restraints takes 5 minutes. Attempting to escape as a standard action adds +10 to the DC.
Catfall (reduce falling damage): Reduce damage by half your Acrobatics check
Balance on ledge (with wall for support): 13
Balance on unstable surface (bucking ship, swaying bridge, etc.): 13
Balance on rope/pole (no wall for support): 16
Balance on point (treetop, vertical pole, etc.): 26
Ledge/rope/point is also unstable: +5
(EPIC ONLY) Balance on ethereal object (cloud, smoke, etc.): 32
(EPIC ONLY) Balance on moving object (arrow, bird, etc.): 32
Failure: (all balance rolls) Fail by 4 or less and you cannot move this turn. Fail by more than 4 and you fall.
Climb onto monster: 22
For each size class by which the monster exceeds the PC: -3
Escape terrible fate (crushing trap, exploding airship, etc. Death by monster attacks does not qualify as a ‘terrible fate’): 28
These options could be tweaked according to taste. Some DMs probably won't want "anime bullshit" in their game like balancing on clouds or whatever. The (EPIC ONLY) tags are to make sure that low-level characters can't pull off any anime bullshit even if they roll a critical success.