Looking at the bad right grip picture.
I would use an automatic center punch to get a punch mark in the center of the broken screw.. When you get a nice dimple in the center of the broken screw, I would get a regular center punch and hammer (couple pounder). Line up the center punch and lightly hit the center punch. The idea is to let the weight do the work, not a big swing. Between making a larger dimple to drill into, you are also shocking the threads, hopefully breaking loose any rust, thread locker or whatever. If you have a center drill, I would start with that. But like an "easy out", if you tip, the drill too far, while drilling, it will break the tip off and you'll have a hard piece of metal in the hole to deal with. Drill deep enough to get a conical hole for the drill bit to follow. As mentioned, a left hand bit would be preferential. I would also
lock the handle bars in place if possible. I've never looked at the 1100 lock system (don't think I ever locked the bars). I do know due to the design of the locking mechanism on some older bikes, a lug the lock cylinder locked into would get broken off in a crash. Thus the bars couldn't be locked.
I think if you loosen the handle bars in the center and slide them to the left, you can remove the whole right control pod and throttle tube/grip. If you remove the center top clamps, use towels profusely to try to mitigate paint scratching.

Take the clutch ass'y off also and use the bench vise to hold the bars while working on them.
center drill example, available at many hardware stores
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