It's a misconception that a closed areaportal doesn't render what you're supposed to see. In fact, the areaportal doesn't render the 'rooms' that the areaportal seal off (when I say room, I mean any space separated by a door or hallway, including the outdoor). If the room has other door somewhere else, you need to close as well.
Not sure if this is your setup, but it's a example:
I'm not sure if this is the best solution for this case, but if you understand how it works, you can seal areas so they start to not render the way you want