I have often found that a broken tip can be salvaged if any of the formed section remains. A bit of light grinding and a pass with a sharpening stone to remove any burrs. The shorter section of tooth is less flexible than the full length version.
Heat, percussion (tap the bit in to the screw and leave it in place), and solvents, all may help. Nail polish remover is mainly acetone, most of the time the missus has some under the cabinet, eh.
Using a screwdriver style handle or a ratchet? I have found that a ratchet with an extension will allow you to see that the alignment is correct, allow you to apply positive pressure to keep the tip from cramming out, and still allow control while applying torque to the screw. Sometimes a little torque in the tightening direction helps too.
All else fails, make nice with a dentist and see if you can scrounge or buy some of his old stock dental burrs. They can be used to carve a slot out in the screw head with a Dremel or such tool, and if that does not work, they can be used to cut away the head of the screw so you can get the pieces apart prior to the fiddly business of getting the remains out of the hole without botching it up.