There are a few different techniques for removing stripped screws, such as the rubber-band trick and using a screw extractor. This approach involves making a custom holesaw that quickly removes the screw using your drill.
You'll need a 15cm piece of a golf club shaft that is cut from the smallest diameter of the club. Cut teeth into one end, which will serve as the business end of your hole saw. Using a wood guide and your drill, cut the screw out. Once the screw has been extracted along with the small amount of wood, use a wood filler and smooth out the surface
Check out the full instructions below for making the hole saw, and take note of the tips they used to cut the teeth as well as how they secured the club shaft into the drill chuck.
Make a Custom Holesaw to Remove Stripped Screws [Fine Homebuilding -- YouTube]