Mine all float, too, and I've never had any issue with moving the thing while palm muting. In fact, it's nearly impossible since in order to palm mute, you have to have your palm above or forward of the bridge pivot posts because they're in line with where the strings leave the saddles.
As far as making noise goes, I've never heard a Wilkie do that. There just aren't that many parts, and they're all well-secured. You might hear the springs vibrate in sympathy, but that's true of any vibrato bridge. You can mitigate that with surgical tubing inside the springs, or foam packed under them.