Here is the second phase of this project. I cut squares of scrapbook paper slightly bigger than the mirror size (just under 4 inches) because there's room for the paper to just slide under the wood. I loved that I didn't have to figure out the best way to glue them in there. I still wanted to have some exposed mirror though, so I didn't cover all of them. And when I was painting, I just slid some wax paper between the wood and the mirror to keep it clean.
The last part of the project doesn't really count as a phase, as all I have to do is hammer in some saw tooth hangers and hang them up. I'll snap a picture of that too, so that at least the reflection of the ceiling texture won't show up in them!