I remember reading either on here or other sites about people having difficulties with sheared off screws and damaged screw heads and trouble getting them out of reels. I came across this whiilst surfing the net, not sure if its of any use to anyone?
http://www.jmldirect.com/Screw-Extractor-PS5616/
I have a set, that that particular one, but a set similar to the one shown. I've only used it a few times, but not on reels. It works for me when I had to use it.