I was able to reproduce both of these approaches. What a relief. Thank you.
Gai - I noticed that if I create a tile component (glue-to, cut-into) and then drag it onto the wall component face, I get the Z. But if I take the tile component from the library and place it onto the wall component face, it works fine.
Alan - I noticed that if I draw a tile on a wall component face, I get the Z. But if I draw a tile onto the wall face and then make everything a component, it works fine.
Ed