That is a very beautiful setup Paddle_grl!
"Where there's a will there's a way" is certainly true. And cats can be perversely skilled at getting into trouble.
I ended up ordering this from Amazon:
Amazon.com: Exo Terra High Glass Terrarium, 24 by 18 by 36-Inch: Pet Supplies
Any orchids in flower (and others that can fit) will go in the terrarium.
When I take them out for watering, I will follow the advice suggested here of pre-emptively locking the cat out of the room first, and staying in the room with the orchids until I'm done watering. Hopefully this will help eliminate further lapses.
There's also been new cat toys included in the shipment (and all the packaging is itself a source of feline entertainment for a day or two).