Thanks! I'm not sure what you mean by pickups binding on the screws. Would putting electrical tape around the screws so they don't touch the pickups be what you mean?
Anyway, the heat shrink didn't go through the holes, so that didn't work. I did put silicone tubing around the screws under the pickups. I hoped that this would dampen the screws, but I hear no improvement. Later this week I'll get some electrical tape.
What DID help was taking out the screws and taping the pickups in the body, wich was an earlier suggestion.
I recorded some rumbling on the strings while muting them. With the screws you can hear (with headphones!) the ringing of the strings between the nut and the tuners, and with the tape that's gone.
Screws:
Dropbox - BartsScrews.mp3 - Simplify your life
Tape:
Dropbox - BartsTaped.mp3 - Simplify your life