I found some Left Hand Turn (counter clockwise) drill bits and have used them for removing stripped screw heads. They seem to work well. On occasion the screw came out before I got the head drilled. I think I found them at Sears several years ago.
I got my LH drill bits at Harbor Freight and they work just fine. If the bit sticks in the screw, it backs it right out. The heat of drilling and the ccw torque of the LH bit usually breaks them loose. If you get the bit centered properly, you will never even nick the threads in the hole.
If the screw stays stuck, I just go up sizes until I drill the screw's minor diameter, the size of the bottoms of the threads on the screw. After that, a tap will usually chase out the remaining trash and I can save the hole and original threads.
This works even with screws bedded in epoxy or 5200. The problem is after getting the screw out of the way, the stupid hardware is still stuck to the deck by the miracle glue.
If the wind is not blowing, I have put wet towels or rags around the offending metal hardware and then using a heat gun warmed the cleat or what ever until the magic glue turns loose. Keep the rags around the hardware wet and the deck will not melt or burn before the glue turns loose. I didn't use the wet rags the first time I did this and had a nasty mess to fix.