Do you have access to a drill press? If so, here is a method that often works.
Get a short screwdriver blade of the right size. Those tips of screwdriver sets work well, as do tips sold for use with power drivers. As a last resort, you can cut a couple of inches off a regular screwdriver and use that.
Chuck the driver tip into the drill press chuck.
Now, pad the drill press vise or get someone to hold the rifle down in a padded rest on the press table. Line the screw up with the driver, and bring the driver down to the screw, making sure the driver blade is in the slot. Hold the press down or lock it. Then work the chuck back and forth. No guarantee, but most screws will come free with this technique. If they won't, there is probably little hope except the drill.
The explanation is that most screws are buggered because the driver tries to slip out, not because the screw won't turn. The drill press keeps the driver blade in the slot and it can't slip out. Either the blade will break, the screw will break, or the screw will turn.
FWIW, the same technique works with frozen percussion nipples, using a nipple wrench in the chuck.
Jim
Jim