Demo of what this does here:
I just had a quick play with this idea and got something pretty close.
Create soft body.
Create armature with two separate bones.
Parent soft body to armature.
Stretch the soft body by moving one of the bones.
This is where it gets a bit limited, but apply the armature modifier as a shape key (I know, you're stuck with the amount of stretch at that point, but trust me, it has some effect and might help).
Keyframe the value of the shape key so that it stetches out slowly over maybe 50 frames, then key it down at 0 about 5 frames later.
Play the animation, and notice how the oscillation of the soft body seems to have been amplified by the quickly retracting shape key.
I really didn't think this would work at all, so having it do at least something made me quite pleased.
See what you can do with that.
I tried keying the deform influence of the bone on and off but that didn't have any effect as far as I could tell.
Nb. I used Automatic Weights. If you don't then there should be a weight painting step between 3 and 4.