[AdamJoshua]

I too would suggest sealing the instead around the glass with a food grade, orderless silicone, I would also do the seems were the pieces of wood on the instead and corners.

If they are that dry I would suggest salt testing your hygrometers to see if they are recording the humidity correctly, are they digital or analog? If they are analog I would replace them with a digital one.

The weather stripping doesn't have to go between the door and the frame, you can put it around the inside of the door so it closes normal but has that extra barrier, every little bit helps.