On the tapping thing...... it works. It works because the hammering or tapping action actually drives the shaft of the screw into the hole momentarily which disengages the threads. The tapping action temporarily "lifts" or separates the surfaces of the inclined plane which is the screw threads.
SOOOO, for it to work it's best that the allen bit be bottomed in the hole, bearing directly on the shank. Then, even gentle pressure coupled with the tapping will let the screw back out. As long as the screw shank's not bottomed in the hole.
On a really buggered one I've degreased and epoxied the bit into place w/JB Weld. For this process I clamp the bit in place tightly overnight using vise grips. I believe that this helps keep from breaking the epoxy bond when tapping.
On this "inclined plane" note..... most folks would assume that "if you break the head off leaving nothing but the flush stub in the hole, YOU'RE SCREWED!!"
Not true
![Smile :) :)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
in fact this disengages the pressure on the inclined plane.
With the head gone the shank is just floating in the threaded hole! Tap it gently.....hit it with penetrating oil..... this is one place where Kroil works because the screw shank is relaxed, there's play between the surfaces. Then you can most often slot it and walk it out with minor screwdriver pressure.
This doesn't really apply to gun screws since the root cause is generally rust but I've found it to be interesting to know. Removing busted exhaust studs has been made less stressful for me since I thought this tidbit through.
And, in any case, if someone put the wrong screw into a hole and bottomed it out and THEN busted it off. You ARE screwed.
![Big grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Now the plane surfaces are loaded and no way to turn it.
al