How do I make the pixellate effect parallax?

I was wondering how I could make the "pixellate" effect not static like it is when you use it ( when my character move, the pixels stay in the same place on the screen ), or is it even possible? I wan't to do a lava effect using a plugin (caustic waves) and the pixellate effect... also the "pixel" are based on the resolution of the screen, and so changing between the types of screens... I tried to use pixel rounding, searched for a mosaic effect in hopes to find a way to fix it... but not a success, I was surprised that no one really bothered with this and I am maybe missing something...

here is a part of the lava so that I can show it

and here is the visible problem:

This seems like a pretty GPU intensive way of getting the effect of just some animated squares. With some ingenuity I think you could do away with the Pixellate effect entirely and take a different approach.

What about using a simple looping, repeatable animated sprite of changing squares. You could do various programmatic things to make it seem more 'random' (picking random frames every so often, or periodically flipping / rotating the sprites...)

Or a tiled background that (while it can't be animated as such) could be given the illusion of 'animation' with some event based methods similar to that which I mentioned above.

This would make it much easier to have the flowing lava follow the screen properly and also make your game much more performant on slower machines.