RHPs can be successfully installed in tubs so they can be safely put into NPI cages. You would need to drill through the top and bolt it in to prevent it form coming loose and you might have some air gaps on the top due to the wonky design of these cages but you can do it. I would highly recommend against a CHE because you would just be ruining the humidity benefits of this enclosure buy putting in a CHE.
You are going ot have to get creative with the placement and installation. Just make sure you are a few inches form the wall and at least 6 inches from the floor. You might have to go with a narrower thus lower wattage RHP to clear the dimensions of this.