I drilled two today. It's a 6/32 screw with not much to drill into. I have a bunch of tiny drill bits and slowly work up to a #36 or 7/64". Sometimes the broken piece will loosen and fall out as you're drilling. Sometimes the drill bit will break. Have a 6/32 tap and an 8/32 tap handy in case you need to make the hole bigger. It's a slow process, but worth it if it keeps you from having to repair the wall. Mine were embedded in brick.
The screw in question is to mount the outlet to the box, so drilling out the screw and replacing it with a larger screw is invisible as long as the replacement screw does not have so big a head that the coverplate will not go flush to the wall. I would drill it out with any reasonable-sized drill bit, find a sheet metal screw that will secure the outlet, and put the cover plate on. 5 minutes maximum as long as you have an electric drill of some type and some small drill bits.
Just a follow up ... tried a drill bit, just couldn't get a grip to push it through. As originally posted, I made more of it than needed. Had to get some corrosion off the back of the screw and then used needle-nose on the back-end of the screw to move it a little, a little more and finally got it out (a quarter turn at a time).
I appreciate all of the replies and ideas. Hopefully it'll help others too.
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