The bits are breaking. Impact drivers will not stop that.
The grip the rings have on the screws is the problem. It is either Loctite causing it or the friction of the screw head within the ring. It will be either heat that will release grip of the Loctite or compressing the rings to relieve screw head pressure.
Impact could help out though.... as it hammers it could fracture the loctite no?
Heat is certainly Tyne best way, though I question what bits you are using if you are snapping them. Either way, a little heat on one of the broken bits if it still fits in the screw head a but, or a soldering iron on the screw head, and a sharp tighten then loosen and you'll have it off almost certainly.