One thing I'm going to experiment with to keep the backdrop from bunching up is to use some scissor clamps to attach it to a stiffer material underneath the area that I will be placing the subject. I got some particle board to use for my last outing, but I ended up on a hard, non-slip surface that didn't really let the material slide much.

Oh, and one place where plexi would have an advantage over the tile boards would be in the case of a black (or any other color backdrop) as the color would show through the glass while still giving a nice reflection.