Correct, screw extractors are meant to fit in a predrilled hole.
Get a few, because they will probably snap before going dull, new drill bits. Start small diameter than move up in size. Just be careful not to drill into the flipper assembly threads. Get a hole big enough for the extractor to bite or as Sana’a pointed out it spins out. This will normally happen with drill in reverse when you’re backing it out. And yes it is a cussing job.