My fridge makes this shuddering sound. Scared the heck outta me at night when I was in my room and not close enough to it to realize what it was at first. Now it's just an annoyance.

They make these green pads that you can put in your crisper drawers to keep the food off the floor of the drawer so air can circulate around it. Kind of looks like a giant Scotch Brite pad. Maybe you could find something like that to pad the bottom of the ice bin to cut down on the noise.