I don't have the maths for this, but what happens if you bump the DCs back up a bit, but only count a serious failure (failure by 5 or more) as a failure, with a simple failure counting toward neither overall success nor overall failure?
Would that make things more swingy, less, or just the same?
Dramatically less, I believe. The math is tricky, because there are now 3 possible results of each roll (failure, success, and nothing). I don't have the time to grind out the numbers, but by both taking good skill characters and making them success or nothing (failure being impossible) and bad skill characters and giving them a reason to participate without killing the group's odds, it would be something of an improvement. Probably too much of one, though, and it could add dramatic length to contests without adding to their interestingness at the table.
IMO, I'd like to see the following changes, which use a similar idea but link it to use of daily resources to "buy" the benefit...
1) restore the footnotes. Skill DCs need to be 5 higher than they are now.
2) add rules for auto-fail (natural 1) so there is NEVER a situation where, on bonus alone, one character auto-succeeds at a challenge, though the odds of 3 natural 1's aren't all that high.
3) add rules to allow expenditure of limited resources to cancel a close (within 5 and not a 'natural 1') failure. AP, Healing Surges (representing frustration and lost self-confidence as success eludes you), Daily Powers (I would limit those to Powers from a Class for whom the Skill in question is a Class Skill, though I would allow it even if this character is not personally Trained in it), and even Daily Magic Item Uses if there's some good story why that power could help. Possibly limit each of these options to once per Challenge (perhaps more Healing Surges).
This would seem to make Skill Challenges more like Combat Encounters, in that they usually end in success but sometimes at a cost in limited resources.