I've decided not to use the glass case for my display.
Since then, I've discussed with Kaavous the issue of holding the screens up on top of my MDF box/assembly, and decided to make steel stands, which gave me more choice of where to place the screens, over the existing stand. I have been working with Rachel in the metal workshop using plasma cutter and TIG welder to make these stands, which have holes on the base to let through cables for signal and power, and holes also for access to the control on back of the screen.
There is a slight wobble when the screens are fitted on, so I'll test and see how they work in the room, and see if I need to add extra support on the side.