What type of screw head, allen, trox std? Flush or above surface?
Apply PB Blaster before trying to turn it.
Smack the screw head a few times to help loosen the bond to the base.
You can also apply heat directly with a soldering iron which sometimes helps.
Head above mount: Is there enough head left to file/cut a new sdt slot? Vice-grips also come in a thin tip version that may allow a good bite.
Last would be to file or moto tool gring of the head, remove everything then work on the newly exposed shank to remove.
Flush fastener: Use a Easy Out Bit, threads bite with counter clockwise torque, removing the screw (or drilled shank). Depending on the taper of the Easy Out and the depth of the stripped hole; you may need to grind down the tip so the sides can bite.
Cheap way, Put the correct tool tip in the stripped hole and smack it a few times to help loosen the bond with the base. Tap in another tip/ std s/d with angled edges and try for a bite using a adj wrench near the tip to get leverage while you press the tool in so it won't pop out.
Alternative: if you have a broken drill bit that would snug into the hole, the broken tip end is what you turn after inserting the other end in the hole. This will give you the correct bite to loosen the fastener. Tap it into the hole, turn with vice-grips or extremely slow with pressure in a drill.
Good Luck.
Good l
By the way DaBreeze, I ended up buying one of the knife sharpeners that you lent me a year or two ago. Thanks for giving me the opportunity to try one before buying. That's what forum membership is all about, helping other members.
Go see JJ.