A broken bolt in a hole is pretty common, especially on an exhaust. Next time, soak it overnight with WD-40, then rotate the bolt slightly back and forth (like a tap) to slowly free the rust. If you force it one way, the rust jams and your bolt can snap. Speaking of taps, that is the only method that has worked for me.
#1. Drill a hole directly in the center of the broke-off bolt, then run a tap down it to cut out the remainder. If lucky, you spare the internal threads. The trick is getting the hole well centered. Start with a center punch and a small drill bit, but not so small it breaks off or you face the problem of #2. Ditto if you break off the tap. I have done it with a hand drill, but if you can mount it to use a drill press, that is best. A few times, I got the metal thin enough to peel it out of the hole with a small screwdriver, without using a tap.
#2. Drill a hole and use a screw extractor bit to remove the broken screw. If you try this, drill the biggest hole you can, per #1, without getting into the threads, then use the biggest screw extractor possible. I don't suggest this method because several times a screw extractor has broken off, then the much worse problem of a piece of hardened steel that you can't drill stuck in the way (ditto for drill bit or tap). Some shops have a "tap burner" which can vaporize the offending piece. Otherwise, you are screwed (pun intended) as I am currently with a valve cover hole in my 383 head.
#3. Take it to a machine shop. They deal with this everyday. I have been charged ~$10 to fix a bad hole in a head when doing other work.
When you re-assemble, consider using stainless steel bolts. Ace has a good selection. The problem is they may tend to loosen, which is the opposite problem.
Re the frozen exhaust bolts. I cut them off a few times on my slant six when the hex edges got buggered up. I used a hacksaw blade held in a rag. You are lucky a slant has loads of under-hood room. I could never do this on my 273.
