Another helpful trick (sometimes)...Fit a screw driver bit to the slot and then put a small amt of grit compound (valve grinding compound) on the tip of the blade.
When you then put the screwdriver blade/tip back into the screw slot it'll be an extra tight fit and the compound will give some extra grab betw the two as you attempt to back the screw out. Hopefully keeping the blade from backing out of the slot.
The driver bit used in a drill press or mill is the best option IMO. Lets you put extreme downward force on the bit so it won't backout and torque is easily applied in just the right amts by hand on the quill of the machine.
Heat helps. Get it hot enough to get some smoke curling from the screw/part junction.
I put a brass, sometimes steel rod on the screw head. Then heat the rod above the surface of the gun and let the heat travel along the rod to the screw.
It avoids putting a flame right on the surface of the gun.
An electric soldering gun works well too,,the pistol grip type for putting some heat right onto the head of the screw w/o touching the surrounding surfaces. (I know it's a wall hanger but no use butchering the thing)
A blob of solder tinned to the soldering iron point helps transfer the heat nicely.
