Personally I would give the dremel method to cut a slot in the broken screw a try first, failing that go round the screw in circles with the dremel and plug with a dowel. I’ve used the second method to remove broken machine head screws a few times. It does leave a largish hole to plug. These guys are a useful resource:
https://plugitwood.co.uk/collections/plugs/products/maple-flat-cross-grain-plugs?variant=31721128820772