To get the best yield out of the material, you might heat bend one sheet in two places to create the back and sides. Then you could vacuum form the tops and bottoms with unique features. Like lamp boxes in the tops and little ponds and places for hideouts or plant and feed trays in the bottoms. You can get creative with the upper and lower sections where the heat bent sides can nest in a groove for gluing and possibly locking in the cages front facing etc.
A straight drape could require 17" all the way around the base of the die, adding 34" to the length and width of the die footprint. Not exactly realistic!
Another problem with any deep draw is the need for lots of draft in the sides to get the part off from the die easier. Also less consistant material thickness after forming. The blank size will depend on the type of forming that can be done. A snap back box will prestretch thicker material, allowing a smaller blank, maybe 8-10" all the way around adding 16-20" to the die footprint.
The excess blank size may be waste of material, but less trouble in fabrication trade offs.