I did a few tests, since this prevents me from actually playing the game. Looks like dragging an idol to a doctor's office will lock all rooms to the right and below it. I'm able to drag again once I take the idol out of the doctor's office.
I meant all rooms to the right and all floors below. You're going to have to place all doctor's offices at the lowers floors and drag idols in order like the image, also wait for everyone to finish before dragging idols again.
