I was able to get a couple of different screws to try. The current one seems to be a #10 x 1/2 inch. If I use a #10 x 5/8 inch, it is tight until it hits a hard stop. It doesn't budge - so the threads in the visor are holding but there is just no more to go in. This is a pointed sheet metal screw, though. I'm guessing the original was more of a flat edge machine screw - so I may try that next. It seems, though, that the problem is not the screw itself but whatever clamp inside the visor tightens around the visor arm.