Like many have mentioned those screws really aren’t needed…they just help keep the rotor in place during assy. You can leave them off… However to deal with your stripped screw…I have in the past used HEAT…and then a small sharp chisel to sort of catch the edge of the screw and try to rotate it counter clockwise with the chisel…many x it will break free and loosen. If that doesn’t work…just drill off the head…remove the caliper and rotor and then you should be able to turn the screw out by hand and replace it. Either buy new ones or leave them off. If you DO replace them…use NEVER-SEIZE compound on them prior to install. AND AND AND…ALWAYS just tighten them by hand with a screwdriver… You will find that they somehow tighten when in use…I ALWAYS have to use an IMPACT DRIVER to remove them. If you use the impact driver they will always come out…if you DONT…you will usually Strip the screw hole out… The impact driver ensures you wont strip the screw out.
My Mazda has these. Not needed a brake job yet, but close. When I was rotating tires, I tried to loosen one to see how it goes; I managed to strip the 1st screw with the 1st twist of my screw driver. This is in rust free CA. I think I will have to drill them out when the time comes.
I can remember when all the American cars came with 2 speed nuts on two of the studs to keep the drums on during assembly, I have aways considered the screws in the rotors the modern equivalent and discarded them like the speed nuts.
Sheesh, the time I spent trying to get those speed nuts off and put them back on again when I could have just cut them off and thrown them away? Guess that was prior to Car Talk. (I’m still inclined to put the screws back in if I ever come across them again. Just makes me feel better.)
I’ll second the comments above about using an impact screwdriver gadget for this. I had the same problem w/a VW Rabbit, that screw just wouldn’t budge using a screwdriver. I worked at it for 45 minutes or more. I finally gave up and headed to Sears. With the $15 impact gadget – I presume this is what the OP means by “shocking” the screw" --I bought at Sears, I positioned the Phillips bit, gave the impact screwdriver a single whack with a hammer, and voila the screw was immediately loose. Took like 15 seconds. Well, plus the hour to drive to Sears and back … lol …
As mentioned above, those screws aren’t needed to hold the rotor on the hub b/c the wheel lug nuts do that. But it is convenient to not have to worry about the rotor falling off and landing on your foot when you are servicing the brakes. So there is at least a resemblance of a purpose for that screw.
Edit: One idea for the stripped phillips head screw. I’ll sometimes take a dremmel tool and cut a deep slot in the head. Often I’ll then be able to extract the screw with an oversized-handle blade type screwdriver.