I would close the top entirely and make it a plate glass front entrance with swinging doors or sliders. Screen tops are terrible for humidity and make regulating temps a nightmare if it isn't in a controlled room. You don't need as much ventilation as you would think. You could make a few 1/4" wide 4-6" long notches on the back up near the top of cage and be good.

Depending on what you're putting inside there you could always staple hardware cloth on the outside for extra strength. Then again, gorilla glue or liquid nails is pretty damn tough with oak/ply.

You could run a few pieces of wood across the bottom front to back to act as ribs and lay a piece of melamine over it to make up the floor (then caulk edges). The wood bracing beneath it would give it support and you would have open sections of melamine underneath to stick your heat tape to.