You'd have to slit the door also, like the door frame, and also slightly bevel the hinged surface so it will clear somewhat as the door opens. It is only going to allow about 30-40 degrees of swing from the closed position before it starts to bind. Does this door have to open all the way for access to the cabin, or is this a cosmetic detail? The other way would be to get some very small brass hinges like those used in music box lids or very fine dollhouses, they hinge like the doors in a house and would permit greater opening. You'd have to trim them to fit and probably pin them instead of gluing. Homepylon's method looks like mine, and works well for the cub doors, but you may not have the thickness to work with.