... I'm going to try the oversized Torx idea first. Then impact driver with extractor. Then maybe we'll get into drilling and reverse-tapping...
For stripped socket head cap screws:
1.) Sock-It-Out
2.) Left twist drill
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https://www.sockitout.com/index.html
Sock-It-Out sets can be ordered through
MSC. Tap on the sock-it-out with a hammer while turning it with a wrench. They work. I can't tell you how many screws I've extracted using them!
If that doesn't work, the next step is a left twist drill. Pick a size that's slightly larger than the hex, but slightly smaller than the screw's head diameter. Either the drill is going to grab the screw and spin it out, or you will break trough the head of the cap screw. Once the head is off, stop drilling or you will damage the counter-sink in the part you are trying to remove. Once the part is out of the way (in this case your mounting bracket) the rest of the screw can be spun out by hand or with a Vise-Grip and some heat.
A set of
left twist drills is must have. Sock-It-Out sets are nice to have.
edit: This may be obvious, but in a pinch you could make your own sock-it out. You will need a pedestal grinder or belt sander and a cut off wheel. First take a larger hex key and cut off the "L" so you have a straight length of hardened hex stock a couple of inches long. Next, grind or sand the tapered lead-ins. The tapers should be fairly steep or your tool will bottom out before grabbing. Also, watch the heat! Either remove the material slowly, or cool it with some water. If you are too aggressive and let your hex stock get too hot, you will anneal or soften the steel. A soft extractor is useless against a case hardened screw.
Please excuse the late - over explanation.