The springs are attached to a block of steel which is attached to the underside of the bridge. If you put something solid, like a block of wood, between this piece and the body of the guitar, this will keep the bridge from rocking. If you decide to leave the springs installed, you should pack something around them, as Raskolnikov suggests, to keep them from vibrating.

When I had a Strat, I removed the springs entirely. I machined a block of brass to snugly fill the hole under the bridge all the way through to the cavity where the springs were, replacing the steel piece. I haven't seen such a thing in any store, so you're looking at some custom work. It would be very expensive to have a machine shop make a one-of piece for you, but if you have a friend who works in such a shop, maybe you could work out a deal. The brass block eliminated any slop in the bridge, and greatly improved the sustain. Steel would work just as well: I used brass simply because I had some.