I don't think an easy-out will help you. The stuck threads are 2 inches below the screw head. I would try using a square shank screwdriver with a wrench as low as possible. Push down as hard as possible and turn the wrench. Two people make it easier. Some valve grind compound or other abrasive in the screw slot will reduce slippage. Maybe an impact driver would work (the kind you hit with a hammer, not an air wrench.) Hope it turns or the head breaks off.
If that doesn't work, some very careful work with a Dremel grinder or a drill bit can remove the screw head. Then you can probably remove the trigger guard plate with the rest of the screw where it can be worked on. This is where you don't want to break it off in the hole. Soak it with penetrating oil, maybe some heat. Use vice grips. Tap on the end while turning. It will eventually come out.
Bruce
