Hello!
I believe, back surfaces culling should be done in screen coordinates! Not in the original coordinates.
Let's discuss the implications doing original coordinates culling may cause.
For example, I am using a perspective projection in a scene like this:

As you can see, the perspective is warping towards the edge of the screen.
This is neglected in original coordinate culling, if I try doing back culling on original coordinates I get results like this:

This scene clearly demonstrates that.