If shifts and shears can be combined to produce rotations, maybe they could produce reflections as well; but this is not possible. Shear matrices have determinant +1, but the determinant of a reflection is -1, and so cannot have arisen from a product of shears.
However, cells can be moved back and forth between two planes while reversing their linear sequence, which is the equivalent of a reflection. Suppose that plane 0 is shifting north while plane 1 is shifting south. Along the x-axis (or any other east-west line), swap the cells from one plane to the other. Northbound cells turn over and head south, and conversely; after 256 steps each vertical column has turned around completely and the reflection has been performed. Strictly, the full planes should be swapped one last time to bring each cell back to its original plane.
Vertical reflection is the consequence of splitting vertical counterflows along a horizontal line; by symmetry, splitting horizontal flows along a vertical line should result in a horizontal reflection. In both cases the mirror coincides with the control line. Even further, reflection in a diagonal can be accomplished by combining crossflows rather than counterflows, split this time along diagonal lines.