Wrestling stuck fasteners is a way of life for mechanics and time has to be spent on that pain in the neck job no matter how proficient the mechanic. Other than what you’ve mentioned, welding a nut onto a broken bolt is an option and in some cases if there’s enough of a nub still protruding a tiny monkey wrench can work them loose.
I avoided mentioning E-Z Outs because while they may work if one is careful, and lucky, there’s also a strong possibiilty of an E-Z Out breaking off in the fastener and then it becomes a double headache.
In some cases there is no option but to drill the bolt out and retap the threads or install a thread insert.