Brian Monetti, I spent several years working in home improvement and construction
Your best bet would be to grab the protruding screw with a pair of pliers. I recommend Vise-Grips, which clamp down and hold without requiring you to keep pressure on the handles the whole time. Channel lock pliers will work as well. Screw extractors tend to be overkill. Iv never had a problem just using pliers, a bit of wiggling, and a little strength. Just be careful to grip the screw really well, because if you slip on it the pliers might dig in and smooth the screw, which will make it harder to grip next time.