Remove screw from lock cylinder
Problem solved. It was indeed a cross-threaded screw as the comments said. I was afraid to get too enthusiastic about using pliers to unscrew it, in case it got utterly and entirely jammed halfway through. The local hardware shop said that in that case I could just take a hammer to the cylinder (after turning the key to where the pieces line up) to break the screw off and tap the cylinder out. So with that as a backup option, I used more elbow grease with the pliers and was able to unscrew it. No hammering required.