we noted a desire to secure the panels of plexiglass to one another
What is the thickness of the plexiglass? I feel like I have seen a clear (non-LEGO) widget, shaped like a really skinny H, that joins flat pieces together at the edges.
I think a similar widget could be made out of wood in a wood shop; and a top railing could be made of precisely routed wood, but these parts would not be clear and might be too brittle.
I think a display building expert would be the person to talk to.