And I'm sure you've set up all the systems that make sure the complicated system is actually working and not dead weight or doing something unintended.
obviously you need a remote motor that spins the sign to "do not disturb" when the meeting starts and then back around when it's over. and a sensor to verify it's in the correct orientation.
so you get the simplicity of the sign with the automation desired by the OP.
A webcam in the corridor that shows your office door from the outside, machine vision reads the image to know which orientation the sign is in. If a meeting begins and the sign is wrong, a little LED on the desk starts flashing red.
They just explained why a door lock has absolutely abysmal reliability.
"Making sure" the complicated system works significantly better than a door lock is actually really easy to do, because the door lock is so bad.