Looking at the motion, or echo, of the effect it seems a lot like some form of radial gradient/ripple. As I recall the time effect is run across a grayscale ramp. Try with one wave expanding out then move to anther collapsing in. It may be two waves blended together but it could be just the one stretching the gradient from the center. It's all wibbly wobbly timey wimey anyways.

shoot high enough fps, and animate a very soft mask all moving throughout at a very fine slit

There are two easy options. Both require that you separate the foreground and background elements unless you want to stretch the whole layer. The next step is to duplicate the layer and then create a mask path that reveals only the part of the layer you want to stretch. Now there are two options for stretching the layer. The first is to set the layer's anchor point on the edge of the mask and animate the X scale of the layer.  The second option, and the one that I like the most, is to create a displacement map with a gradient. White moves the pixels the farthest, and 40% gray does not move the pixels. You can then animate the gradient or animate the x offset to create the stretch.  A little mask feathering and animating the colors will do the trick. Here's what that looks like:If you use the Displacement Map workflow, set the project to 16 or 32-bit.  I've uploaded a project file. You can substitute any of your own footage.