Uffff soque la tienes difícil amigo.
En primera no se fregó la rosca, lo que se rompió fue la tuerca fija, rosca es cuando se puede desprender y llevar hasta la cuerda del tornillo.
En ocasiones me ha pasado y dependiendo la calidad y rapidez con que se quiera el trabajo así es la solución.
Si no requieres de estética, reemplaza los tornillos por pijas o chilillos que agarren directo al plástico.
Si quieres algo más profesional deberás encontrar la forma de adaptar tuercas para "madera" o tuercas de empotrar.
Son como estas:
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6B1LeQykX1kbXGOOXZVJPi0v8AhNI3y7FSCABpc3PInTfbWaj1QbqhzN1Hsj385j/gHYfWOT6zMqW0GwG8yqQ7LcSOCaw8St7YPMj7QPIzqGGxC1FDIQynYj97z8/4rjoFUAexsG6nmfSdL+jviwbNTvoRmX1G/wC/KFi9REQpERAREQEgu0XCDU+spjxgeJfvgf8AcJOxA5zTb9/vnPTSy8b4DnJqUbBz7S/Zfz8m85WCSpysCrcwRY/8xGa1sZgqVVctamlRbWAcXt6Hce4yoca+j9fawjWP+TUN1/01d/cwPrLzaDKih9mextU+PFHuwDpTUgsfUjRR56n8ZeqdNVUKoCoNlXQDr7/M6z6DPpEYry0x1WyqWPKZC4Gp/UnyA5nyk/wXs+Sy1a4tl1p0jyPJn/m6Dl67Qb3ZXhxo0buLPUOdh008K+4fMmTURDROCduOBnD4yplFg5uPfr+H4TvcrvbLs8MXTuo+sXbzHT16f8yxLNcHq08tusleAYBqlZO7OVgwPUC3XytPHF+EVEYlgdDa9tvXoZYezVDu0LXsxFgefmZLWIs3FXRVV0UG+hVTexHS9tJEVuLUaZGdjSvzYG3pmFxPQx5pBrMQG0y9fjLT2O8YLNSQNsWscxG4uCSOckrSqntBQJ1xVO461ACOfM3G8xtxugxt/EIx6Bsx+Uvnarg9CrSJqUabHkzU1YjnoSLjblOVNw+mhsoW3iIy8wD4b/Gb6RJ1sYlvCC5/2j4madYs+hsB90be885jpm46TNmv5TnfKtYrHGMDlP8AKflJ/wCiarU/jlTdQrG/qCIxGHDi0un0Zdmu5DV33bRf30kir/ERNhERAREQEREBMOJwqVBZ1DDzF/h0maIEBiezCHWm7J5Hxj56/Oaf/TFT/MS3LQ/hLXEamKp/0xU++nwM90Oyzn/EqgDpTXX/AHNcfKWiJdMR/D+DUaJzIvitbOxLN8Tt7rSQtESKREQERECM4lwVKpzDwVPvDY/1DmJVuK8CZfaS38yC6+8cvlL5EDlNThrEjZll+7M4YJSsLW2GpNhy39Zu4jhtJ/aQX6jQ/ETSHAQuqVHU+4/pGIydoSe6Ol9rzkfElZahA+81+h226Tq9bhNVv/cH3g/+UjX7HZjdnX/6yT83l6HO1W3rebVDBs1goNzyAJPuG5nQcP2Oor7TMfIZVHyF/nJrBcPpUv8ADRV8+Z9SdTMeqqnwHsfs9fQb5OZ9TyHlvLoiAAAAADQAbCeomgiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiICIiAiIgIiIH//Z
Las encuentras en cualquier tornilleria que se respete.
Saludos