Pixel based rotated pixelate?

I'm working on a pixel based halftone filter where dot size is image size independent.
However I ran into a problem: I can't do a pixel based rotated pixelate effect.

Here is what I'm trying to achieve:

This example is not pixel based and works like this: I rotate the image, feed it into checkers, rotate it back.

Right now I build rotated, pixel based lookup coordinates:

(Cell size is set in pixels.)

However this will also rotate the source image while sampling. I tried rotating it first then sampling it then rotating it back but the second rotator node doesn't do anything, probably because the way the lookup node works.
I also tried to apply the manual, pixel coordinate based rotation to rotate things back but that doesn't do anything either.

I'm not sure what to do next...

Oh, I recognize her, that's Mathematica's Lena!