Pics of the specific configuration would be helpful.
In the WORST case, drill off the head of the booger'd screw using a sharp bit slightly smaller in diameter than the screw head. Go SLOW, so as to minimize contact with the mount when breaking through; you will feel the screw head come off.
You will then either have enough residual screw sticking out to GENTLY get a hold of it with a pair of small needle-nosed Vise-Grips to rotate it out or not.
If not, break out a tiny drill bit and VERY CAREFULLY drill down into the CENTER of the stub; if it is not a blind hole and you can get all the way through, then bonus points towards eventual success. Select the appropriate tiny extractor from your tool bin, and cross your fingers.
If it comes out, then chase the threads with a tap, and get a replacement screw.
I went through this taking a rail off a precision bolt gun recently....very nerve wracking, to say the least!