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JB wouldn't work, as strong as it can be it doesn't take much to crack it and have it break. Dremel or vice grips are you're best bet for stripped screws.
But what if there is no room to fit a vicegrip or a flathead?
i have a stripped, rusty bolt holding my thermostat housing and theres pretty much no room for either of the 2.
I dremeled the tip off when a fender bolt got focked. It was a waste of time though, it takes too long for me. Then i just vise griped the screw out - if you do this, screw it down, not up, I stripped the lower threads, so it wouldnt go out all the way. Then i screwed it going down too. So imo, a big waste of time. Just dont strip thebolt in the first place