Is the one that's broken below the gasket surface where you can even line a drill up on it? If you can, perhaps you can try this:
Buy or make a bushing that fits the manifold hole and centers a 3/16 or 1/4 drill bit. Install the manifold so the bushing centers the drill hole over the center of the stud. Then drill with left-handed drill bit. Might just back the broken piece out. If not, you'll drill your way to a centered hole for a screw extractor.
These exhaust fasteners don't break because they "twisted off" but because they were stressed side-to-side repeatedly by the manifold heating and cooling but at a different rate than the head. The broken piece may be rusted in place but not galled in place like one that broke by twisting.
