No doubt, a real serious challenge! I sure don't envy you! Rather admire you for taking on this challenge! I'm wondering about that approach of successive drilling of increased size bits, removing the reminder of broken bolt, then maybe instead of being too concerned with having enough of the original threads remaining, just plan on drilling it out completely to the correct size to tap it and run either a "Time - (Ok, this damn Apple won't let me spell it the rite way!). It is called a "time" - followed by the letters "s", "e", "r", "t" or you may prefer to use a Helicoil. Just my two cents, not to conflict with or contradict any of the great advice previously given you. Of course the way I'm suggesting does hinge on whether or not there's adequate material there to drill it large enough and tap it. Best of luck and will be looking forward to reading about your progress and success!

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Dedicated to the preservation of antique Mercedes Benz's, one rusty ol' bucket of bolts at a time!