New answers tagged screws
It looks like you should be able to use a small flathead screwdriver (or an awl, or any flat bit of metal, really) to push up on the plastic surround while unscrewing the screw. This might just about push the screw up to remove it. Or, you can push the screw up with an awl or flathead screwdriver, and grab whatever protrudes with a pair of needle-nose ...
First, you need the right sized screwdriver bit - this is already looking chewed up as though it's met not quite the right size. This is one area where getting the non-Chinese product may pay off in the long run (they not only work better, they also destroy less things you work on, so between not having to throw out and replace the tools and not having ...
There are "screw extractor bits" that are made for this purpose but I'm not sure they make them as small as you might need. You can also try placing a thick rubber band, latex glove or dental dam between the screwdriver tip and the screw. A drop of super glue or epoxy on the tip of the screwdriver is something I thought of once but never got to try it.
An easy-out would do the job, it's a bit of an overkill. Have you tried taking a small screw driver (flathead, it will have to be smaller than the hole) and jamming it into to the broken plastic screw and trying to get it to back out?
A left handed drill bit a little smaller than the thread size. Be sure to run the drill the correct direction for a left handed drill bit. The idea is to drill it out with a drill turning the direction that will tend to unthread it. If it is stubborn and does not unthread during drilling, use a screw extractor on it (the straight-splined versions (a) ...
Sometimes cutting a new slot for a larger screwdriver in the screw head is all that's needed to get a stuck screw out. A hacksaw, file, or moto-tool with a cutting bit, can all be made to work in some circumstances. Cutting too deeply, or trying this on too small a screw can leave you with half a screw-head when you apply torque.
My suggestion: Use the hammer at will. After breaking the concerned parts (and eventually some of the involving wood...) and getting rid of screw's head (the remaining can stay in its place...), use generously epoxy glue. Go straight to the closest mirror and admire the face of Einstein after creating the Theory of Relativity: everything is relative.
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