Anthony, XB has a very good point. This seems like the best idea yet. I know it will set you back completion-wise but doing this will probably lessen the damage to visible parts.
I apologize if you already know how to do the following, I know how to do it because I’ve screwed the pooch so many times I shouldn’t be wearing pants.
Depending on the thickness of the piece being held, once removed, you might be able to grab the protruding screw-shank with locking pliers.
Or once the red-piece is removed, slot the shank with a Dremel tool.
The “minor diameter” approach expanded: with a cheap vernier caliper from-harbor freight, Lowes, Home Depot etc., measure an identical screw’s smallest diameter. Lock the caliper then find the drill bit that fits tightest in the vernier’s jaws.
Smooth the protruding screw shank as best as possible. Center punch the exact center. A cheap spring loaded punch will be very helpful here. Marking the target with a felt tip pen is recommended.
If the spring loaded punch makes only a small dent, a hammered punch will now have a good seat. Spend time aligning the drill bit (in the drill) with the screw; get a good idea of what straight looks like from a couple of angles. If the female threads are in a through hole make sure not to damage something behind them as the drill passes through the screw.
Now only the screw’s male threads are left in the hole. Identify the proper size tap. With a cheap a thread gage measure the identical screw’s thread pitch. Get a good quality tap. Chucked in a drill, the tap can be guided better than with a tap-collet. Don’t pull the trigger!, just hand-twist the chuck, every few turns reverse the chuck to clear material. If the female threads are in a through hole the material will be ejected a bit better.
If you end up making the hole too big a heli coil can be used.