Experimented a bit more to try to figure out the problem, the orientation is only not mirrored if I am replacing cubes with a block that has orientation. If I have wedges that are already mirrored then when I replace them with the proper lines of symmetry still in place it works. For some reason the rotation information isn't conveyed when the block being replaced is a cube. (Let me know if I haven't made sense and I'll take some screenshots or make a GIF and it should make more sense.)

Yes, I've now tried turning it off, but the same problem happens.

I just loaded my game again. When loading and pasting from the template all 9 display modules are now displaying the correct text. However, still only 8 of the 9 original display modules have the text and none of the duplicates that I pasted yesterday.