I fabricated the internal pressure plate and left enough on the top to form the handle. The pressure plate easily flexes out of the way (riveted at the top and free to flex at the bottom), but is designed to pinch paper at the bottom of the tray as well as the top.
Next I'll make another shorter pressure plate for the top so there is a gap along the top edge. That way I'll be able press the map down into the slot without using the other hand to pull the handle out.