Can you get a drill in there? A left handed drill bit works wonders(heat, vibration, and removing material so the rest can relax that .0001 of an inch all at once). Many times the bit will back the damaged screw out without further effort.
If you have the room these work pretty well. Similar to the left handed bit but more specific. Again, you need to get a drill in there. I have a set but it's been a while since I've seen or used them(very full and disorganized shop). I don't remember cursing and launching them across my shop so they must work ok.
https://www.google.com/search?q=sear...33029324074281
I'm sure you already know this but it might help others. When drilling use a good center punch to give your drill a good starting place where it won't wander. Use a very small sharp bit to start, then go up in size.
If you screw up the threads in the hole you can drill and tap for the next larger size by the look of it.
Sometimes heat helps too. Try a hot soldering iron on it since a torch is out of the question.
I hope this helps,
Rodney