I used a vanity mirror clip at the bottom of my monitor lexan.  You see these at the bottom of most bathroom mirrors, the metal strip that runs across.  It came in a 6 foot length, so I just cut it down.  I still need to paint it, right now it's bare aluminum.  So that holds the mirror from the bottom.
For the top, I got some window screen clips, and screwed 3 of them into a strip of 1x1 across the back edge of the speaker panel, where the top of the lexan meets.  This way I just swing them down to secure the lexan, or flip them up to remove the glass for cleaning.  Super easy!