Compositor Translation mode "Factor"

Hello! I am currently trying to create a VHS-type effect so if need be i can overlay the proper nodes onto an input, and to learn about the compositor in general. Here is my dilemma, I have everything looking how I currently have a texture that is to be used as a factor texture:

And I want to be able to translate the pixels in the area with black just a smidge along with varying the amount of translation all the way to zero, following the gradient on the image. However, my idea was to just use a mix node to mix the translated image and the original image but only in the black areas however it didn’t give that “falloff” type look. So I have to scrap my plan. Any ideas on how to accomplish this:

Except in the blender compositor?

I have Blender 2.79 and am using Blender Internal

Instead do the Mix between the black bars image and a white image. Then you will have an animation of the skew effect instead of a dissolve between them.

Hey, I’m not sure I quite get what you are trying to explain. Do you mean something like this?

Where the Alpha over node is the comp output? Because doing this still gives me a result where the output looks like a dissolve between the two.

TBH I can’t quite make out what is going on in your nodes. Can you post a more complete version?
Anyway here is my version, you can simply animate the Green value to get more or less distortion. I have built in a wrap edges effect to compensate for the lateral distortion (no black borders).

The red node allows you to change the shape of the distortion produced by the texture.

I have just realised that if I invert the texture values then I can only offset the distortion instead of the whole image.