Func_door is easier if you know what you're doing. Note that you do not need origin brushes for func_doors, only for func_door_rotating (and trains and stuff).
Just use a normal brush, assign a negative lip value (that many units it will go "beyond" the brushes length) and set the crush damage to something ridiculously high.
Alternatively, you could make a trigger_hurt around the door and trigger it exactly when the door closes, again with ridiculously high damage.