One of the most important things in removing "stubborn" screws, (especially decorative engraved screw heads on expensive guns), is taught in gunsmith school, whereby it is required to have a large selection of special custom made "gunsmith" screw drivers; or, milling & providing a custom exact fit for the head of the screw driver into the "stubborn" screw slot.
1. Screw Driver Thickness:
A. When a screw slot is wider than the screw driver head thickness, all of the pressure is placed on the two (2) ends of the screw slot; hence, the ends of the screw slot receiving all of the force get deformed, (buggered up), such that the sides of the screw slot are no longer parallel.
B. When a screw slot is the same width as the screw driver head thickness, all of the pressure is placed uniformly along the screw slot; hence, the ends of the screw slot do not become deformed and the sides of the screw slot remain parallel.
2. Screw Driver Taper:
A. Most new screw driver heads are "screw-up" by having a tapered head; hence, the "tops" of the screw slots receive all of the pressure, get deformed, & again, the sides of the screw slots are no longer parallel in the vertical direction. Also because of this tapered wedge effect, the screw driver head moves upwards when pressure is applied & slips out of the screw slot.
B. If one has a custom manufactured screw driver, or if one mills & removes the taper from the screw driver head to where the screw driver head has no taper, & the screw driver head fits tightly in the slot, when pressure is applied, the pressure on the sides of the screw is uniform; hence, the tops "and" ends of the screw slot are not deformed.
3. Screw Driver Alignment: The use of a drill press greatly helps to maintain correct contact between the screw driver head & "all" of the screw slot, & prevents the screw driver head from slipping upwards out of the screw slot.
Hope this helps someone in removing future "stubborn" screws.