I use a Snap-On stud remover with a collet designed for that thread, tightened as tight as I can get it. Then let a 1/2" impact "lightly" hammer on it to break the bond loose. A breaker bar and socket will just twist and break them. You want that light hammering too loosen them. That worked for three out of the 48 studs on this clock.
Then I mig weld nuts to the broken ones. Grind the plating off the nuts and washers or buy un-plated ones. The plating contaminates the weld, and it won't be as strong. We did this at work a lot on the trucks and we found we had better luck by removing the plating. Two of them came out and one of them refused to after I broke several of the welded nuts off. As you can see it's hard to get the mig wire down in there that deep to get good penetration on the stud so first what I do is first weld a thick washer to the stud and then weld the nut to the washer, filling the entire void with weld so that heat will travel down into the threads. The mig weld will not stick to the cast iron, no worry of messing up the block. Not everybody has a mig welder so that leaves the drill. You can see how the coolant (actually lack of the green stuff) got around the stud and electrolysis and corrosion ate the block. It also glued that stud to the block.
I just got a call and need to leave but I will post more photos of the welded studs and the drill guide bushing I use to take out the the one stud.