Wow that is an intense landlord! I have never had one inspect and even if they wanted to come over to talk to use they called in advance. Laws are probably a lot different and vary state to state then ours in Canada.

If told to get rid of the snakes would you have any family or friends you trust that would look after them for you until you are out of your lease? It may be worth thinking about as a last resort if inspections are going to occur or have already. I think opaque tubs would do the trick though and I am sure their are laws protecting your privacy so he/she can't go through your personal belongings.

How hard would it be to put hinged doors on your rack with vent holes and a lock? If it's locked, they can't inspect. Just make sure you drill some air holes in the doors.

Another option is to put labels on the bins that would deter the wanting to open like "adult toys" etc.