I still think that you are misunderstanding what's happening. The problem isn't that the screws are wiggling. They are screwed into the body. What's happening is that the whole pickup is wiggling on the screws, in relation to the body. Meanwhile, the strings are sitting still. This movement of the pickup in relation to the strings is what is creating the microphonic signal. It's almost like the strings moving above the pickup, like normal operation, but reversed. The screws themselves are far enough outside of the pickup's magnetic field, that they aren't going to create signal. Changing the screws to brass isn't going to do anything. Unless the brass screws fit better.....
Now, if you wrap tape around the shank of the screws, so that you are filling the gap between the screw shank and the hole through the pickup, that will do something. That will help keep the pickup from wiggling. But the better fix is to add a foam pad or better springs under the pickup, to push it up against the screw heads, and prevent it from wiggling and wobbling.