If I understand correctly, your suggestion and Glenn's both require you to twist the plastic all the way to the end of the chord to correct the kink. Is that right?

That doesn't make sense to me, and every time I've corrected it it hasn't required so much work. Logically, it didn't take twisting the length of the cable to get it kinked in the first place, so reversing it should be just as simple.

Unfortunately, like Jeff I've been cordless for a long time, so it's been years (maybe 10) since I've had to do this on a regular basis. Maybe I'll see if there's an old phone chord like this somewhere in my stash...