I would use the Gorilla glue for sure. Use is sparingly and make sure you clamp it tight. The glue is polyurethane based and will expand as it dries to get into all the little nooks and crannies. Works great and is waterproof when dry. I doubt you will have enough meat on the drawer to get a screw in it without splitting it more. Wear latex gloves when working with the glue. If it gets on your skin it will take a couple of days to wear off. (personal experience first time I used it).
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