If you like the tambour, simply carefully remove it from its tracks, get a piece of unbleached muslin and a can of 3M spray contact adhesive. Lay the tambour on a table or workbench face down, measure the muslin to within an inch of the edges where they slide in the tracks, cut out the muslin, spray the glue on the back of the tambour and one side of the muslin. After the adhesive dries, place it on the back of the tambour and press it onto it. After it sets, replace it in the track, and continue to enjoy your tambours.
Meddle not in the affairs of dragons, for you are crunchy, and taste good with ketchup.