feel like overcomplicating a door? well here's your chance!
for each side of the door actually use 2 func doors one pareneted to the other. Much like Piston lifts where the pistons expand and contract.
Lets call them Base Door and Func Door as the Base door has no models parented to it, only the Func door. The Func door has the actual door models parented to it.
Now each kind of door would move the door models a little, if you only opened the func door they would stop half opened since the actual doors are thinner than the door model.
Place a trigger in the doorway which is only triggered by the cube, make this trigger disable whatever mechanism is actually closing the Base door, so only the Func door closes, and seems to be jammed open. I usually close doors by Endtouch triggers on either side of the door, you would need to make a seperate one for the Func and Base doors in this example, then just disable one for the door to no fully close.
Hope this helps, note that this idea has not been tested but was thought of on the fly 