Just use your imagination. There's probally hundreds of ways to achieve what you are looking for and you might find something in your home that will work.

But yeah....paper is too weak and cloth holds moisture. You would be better off using some thicker Boss wood.

I'd imagine duct tape would work great as long as you double tape it.

To get tape to stick most effectively, clean the area you are going to apply the tape with (let it dry).

Then run the tape all the way down the gap. If part of the door hinges are on the outside you might want to cut little slits in the tape where the hinges are so when you open the door, the tape will remain where you places it.

The final trick with tape is to take something flat or has and edge (credit card, back side of a butter knife, a block of wood, etc etc).

Start from the top and press down on the tape.

Run the item down the tape line to get all the air bubbles out of the tape. This will create the best bond between the cab and tape.

I've used that method for a small cab I built for someone who was using it to grow strawberries and it worked well.

Best of luck!