Well I'm probably over-complicating this but I am trying to visualize the problem so I drew this.
Since each dimension has a contribution to the total Normal force, their magnitudes and directions need to get combined, right?
Am I thinking of your proposal wrong if I split the block in two, one left and one right of the center when its opened to 180 degrees?
Normal Force = (m/2)g*cos(Theta) + (m/2)g*cos(Theta)
N = mg*cos(Theta)