I just spent the week removing 96 (!) severely corroded pipe fittings from a plastic injection mold. Exactly ONE unscrewed without being drilled and using a screw extractor. The other 95 put up various amounts of resistance, and one had to be drilled out and the threads picked out one by one. I've been doing this stuff for many years, and have a variety of tricks.
I like the square extractors much more than the spiral ones. You use a tap handle, as others have pointed out to give a balanced torque. It's very easy to snap one off pulling off-center with an adjustable wrench or pliers. The cheapest Harbor Fright tap handles work just as well for this use as a $100 Starrett.
I always start with penetrating oil- Kroil or PB Blaster. If that doesn't work, then heat. If that doesn't work, then heat, and then penetrating oil. Although a bolt can be fused in place pretty bad, once the head pops off, at least you're not fighting bolt stretch. I've seen bolts walk right out after the head popped off. Rare, but it happens. A square screw extractor can take a surprising amount of torque. It's downright scary when you can actually feel it flex. I have the advantage of working in a tool room, where there is an EDM machine if all else fails.
If there's room, welding an extension on the broken bolt works wonders. It gives you something to hold on to. and the heat may loosen things up. Sometimes tapping (Okay, pounding) on the offending fastener will help break up rust and other stuff.
I've broken taps and screw extractors when I didn't have an EDM or carbide drill. With enough determination (and safety glasses) you can shatter them and dig the pieces out. Sometimes these things can take all day! I've also drilled the entire mess out with a hollow mill (like a miniature hole saw) and pressed in a plug to replace the impossible fastener. Good luck!