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I say use an easy out, they usually work well, its just getting your hole centered that is a pain. Good luck.
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Easy Outs are very poor (usually worthless) for removing any really tight broken bolt. By it's design, it expands the hole it is in & makes the stub even tighter in it's hole. The LH drills that are mentioned work much better. By nature, the drill grabs at the bottom of the hole & tries to unscrew the stub. If you use progressively larger drills, the stub unscrews out of the hole fairly soon.
D