If I understand you correctly, you want a look something like this?

It is possible to make this a little more extreme...
To the image I applied a Filters > Distortion > Bulge. Normally you would think bulge would "blow up" (bulge out) the image, but this particular version, if you go with a Scale greater than 1.0, the image is actually collapsed.
I tried different behaviors with this, but it was better just to keyframe the Scale parameter.
This is the general shape of the keyframes to emulate a "punch":

The first (leftmost) keyframe is set with Bulge > Scale = 1.0.
The second (middle) keyframe is set with Bulge > Scale = 1.55
The third (rightmost) keyframe is set with Bulge > Scale = 1.0.
The "reflexive" animation is created by making all three keyframes Bézier interposition.
The left side control points make almost a square corner. The right size has a little bit of a "bounce" applied — Control point from middle point pulled far under the 1.0 "level" of value and the right Control point is upward at about a 45º angle so there is a small oscillation.
The Bulge Amount value for my example is set at 455 and the Center is 0,0.
To make this more extreme, you can set the middle keyframe to values > 1.55 to about 2.0. I wouldn't go much further than that. You can slow down the animation by spacing out the 3 keyframes a few frames more... but the relationship between the three should probably maintain proportion.
HTH