[Zeke]

Dremel the screws and then do what others have said, thread in headless screws and push then into holes drilled for a tight fit. A little glue of almost any sort should do the job and a clean threaded shaft is the perfect situation for glue other than really thin instant glue. You can also put a little glue directly into the new hole with a Q-Tip. If things are a bit sloppy, wet the inside of the hole and coat the threads with Gorilla (polyurethane) glue and it will expand. Just need to coat the tip of the threads and tape in place to hold the angle you need for a couple hours.