couldn't we have a webcam to stream/record the video? or perhaps capture snapshots? If needed we might subtract the human from the video stream using some basic machine vision techniques.
Exactly my thoughts when I saw this. The problem with writer obstructing the view can be solved by place the camera behind the board and using a translucent white plastic sheet for the board. If the front of the board is illuminated well, then the camera shouldn't have any problems in capturing the stuff being written on the translucent board. Mirror the image in software and you are done!
I imagine the human's hand would be obstructing active areas of the board a large percentage of the time