So how can 2-point clipping be visualized nicely in 3D?

That picture is to be understood as a full binary tree: The two lower left views are descendants of the view above them. Note any inconsistencies? Well, I actually had 7 instances running with the same scene in all of them :P
One of my bindable "commands" is to deselect the original brushes, and there is a complementary command to deselect the copied brushes. In clipping, I misused that mechanic a little, but it turned out practical. I originally added that mechanism to quickly deselect the original or copied brushes after, well, copying brushes on the fly. Internally, those are just two lists of brushes filled after copying them, that easy to use for clipping too. In this case, the "originals" are always the ones behind the front face, and the front face is always shown in the normal (unselected) brush color.
Like all the other commands, clipping works in click-and drag mode (that is, you perform a full clip by pressing the clip key or mouse button down, moving the mouse, and releasing the key or button), and in two-click mode (that is, you release the button without a valid clip plane, to place the second point with the next press). In the two-click mode, one can fly around and reposition the grid without interfering negatively with the active mode. One could start making a box here, fly to the other end of the world, and end it there. Every mode can be canceled by hitting a key that doesn't trigger a non-interrupting grid function, so when you are panicked, you can always cleanly abort what you are doing.