HEre's how you do it.
Keep the original door. Hopefully it swings out, if not it will just require more space. IF it swings in , leave enough space for the door to swing into the closet, then create a plastic door with plastic or trash bags or something more sturdy like some of the reflective surfaces you can buy at grow shops. Cut holes in your plastic door for ventilation as describe in this post. Also leave enough for the door to close (more like curtains probably.)
When you need to be stealth at the last minute, just turn everthing in there off and close the door. (make sure you have a swithc handy. This could even be a surge protector.) Throw some dirty underwear on the doornob to discourage anyone opening it for any reason.
This way, you can have a good odor filtration system/exhaust and intake and still keep the door as is.
If youd on't hae proper odor control, even with the closet door, you'll be able to be detected. That unexpected trip from the landlord could be bad. With odor control, he won't have any reason for even thinking about going in the closet.