So, in case it wasn't clear before, the reason welding a scrap nut or bolt to the broken part is to put heat into it, which loosens up any adhesive or rust. It is my number one choice for extractions, and I have a whole chest full of extractors of many types as well as the experience that comes with reaching a point where I get to say that I have a chest full of extractors of many types. Those come out depending on the situation, and only after heat has been applied and failed. Since it is a left hand screw, I'd choose a straight fluted extractor. They work exceptionally well. Either you will succeed, strip the stuck bolt or you will break an extractor. Technique, heat, and penetrant all help, but in the end it's also a healthy dose of luck that gets you free. Using a reverse-twist drill is a bit of a hail mary, since it only works a small percent of the time. Grabbing any remaining fastener with vise grips has been significantly more successful for me than any other method when it's been possible, save for the tack weld trick that is the king of the hill for me.