Frame by frame animation
You can use shape hint or bone tool to animate this object.
Please see the below tutorials.
Those videos are basic tutorials of how to use the Bone tool. But that wasn't my question. I already know how to use the Bone tool; what I don't know is how to make it not produce junk when animating curves.
And boy, it would be nice if shape hints worked, but they don't. Shape hints are for shape tweens. They aren't available for IK. And converting the IK to frame-by-frame also won't enable shape hints, because frame-by-frame isn't tweening. And of course, once you do that conversion, you can no longer adjust the motion (at least not without difficulty).
So perhaps the answer is that after 3 major versions of Flash that has IK, it simply won't produce acceptable results with curved shapes.