As aldiaz stated its very rare for a complete panel to pop out unless the tank was built using the wrong glue/acrylic.
X2 on gluing acrylic strips into the inside corners.
Drain the tank clean all the inside corners good. Get some 1/2x1/2 square stock and glue them all in with weld on 40
This is an interesting idea. Maybe a new canopy and stand could be designed to cover over the bracing.If the effort is made to drain and reinforce, it may be worth applying an acrylic 3-4" width 1" thick bracing around the entire top and bottom perimeter. Similar to eurobracing on glass tanks. I dont think the bracing would look bad either if done right. I've not done this but have seen it done and food for thought.