Chris Fleming wrote:The only thing I can think of would be to carefully score the top of the screw til you make a line deep enough to use a small screwdriver to get it out. I've got a small artist's etching tool that I've used for a similar problem, but I'm not sure what you'd use. Maybe try a few things on the other half of the screw to see if they can scrape into the metal well enough?
Tricky wee problem though
...You might be able to cut a slot into it with a small diamond file or if the area will be covered by the pickguard, then you could remove some of the material around the sides of the screw until you are able to grab the screw remnant with needle nose or similar pliers and unscrew it, then fill the opening with "JB Weld" wood, plastic wood, wood shavings and glue or the like. If you decide to remove by the second method first set the pickguard down in proper position and tape masking tape along the pickguard's edges. This will provide a boundary so that you don't remove material that will be exposed beyond the pickguard's edges and will also serve some protection of the finish as you work on getting the broken screw out.
Someone else may be able offer experience with adding oil or some other type of lubricant to facilitate the removal.
Could you borrow a power drill and some drill bits from one of your mates? A power drill and a 1/16" or 1/8" bit would allow you to drill straight down beside the broken screw, then you could just push the screw out sideways into the opened area. You might have to drill one to three holes( C-shape) pattern to facilitate this. Does this make sense?