I was thinking of this same idea yesterday.
I was contemplating using either sheets of acrylic adhered to the walls etc, or picking up some cool vinyl flooring (like we have in our bathroom) and doing wall to wall and on the wall flooring. The stuff we have looks and kind of feels like slate/stone (not slippery or shiny).
Then replace the closet door with the screen door.
I was thinking of framing out a drop ceiling with aluminum screen so that the fan, lights and mister would be out of reach of the chameleon (which by the way we don't even have yet ). But anyway those are my ideas up for critique.
The other idea was to use our walk-in shower that no one ever uses and replace the sliding shower doors with sliding aluminum screen doors and enclosing the top with the screen as well. This would take considerable nudging to convince my spouse though .
I dont see why it would not work... However you would need to do several things to make sure that you would not destroy the walls and floor. Install a fan to keep the air moving, Build a false floor so you can have some drain area and cover the walls. So some simple stuff like that and I think you would be good to go.