Hi Mate
When I use to work in an exaust shop we had broken studs to deal with all the time prob harder as they were rusty on cars the ways we got them out was a bit of heat around the stud trying not to heat the stud then use vice grips or stud remover both work . If that fails drill a hole around 3/4 of the size of the stud and use a ezy out or if you dont have a easy out a self taping screw srewed in realy hard then heat around stud . If that fails drill hole out to same size as the inner thread then you can pick out the rest of the thread but your hole needs to be right in the middle .
Hope that helps .