Have you tried the pole in the door track to keep the sliding doors closed? If the pole is a metal pipe, it should be too heavy for the cats to lift out of the track. Forgot to mention this in my other post about the shoes.
Your shoes are unwearable as they are. Try washing them in warm water in the washing machine on the gentle cycle with detergent and Oxiclean or a box of baking soda. Then stuff them with newspaper or plastic bags to hold their shape while they air dry, preferably outside in the fresh air. If shoes are suede, brush well to raise the nap. This has saved leather sneakers, mary janes and ballet flats for me after my cats used my shoes as a litter box. Hope this helps you.
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