If you don’t mind buying another tool - there are unscrewing tools, which you apply like a screwdriver and hit it with a hammer. They form a new cross-slot profile in the screw head and at the same time give a rotary impulse to loosen the screw.
Anyone know what they are called?
Edit:
That’s true but they annoy you with a persistent banner to add an email address later on. But it’s working nonetheless.