What you are experiencing what is known as "Stratitis". This is where the magnetic pull of the polepieces affects the strings as they vibrate. This happens with traditional single-coils because the polepieces are magnet rods so they have a direct interaction with the strings. You don't hear this with humbuckers because the magnet is a bar that is in contact with the polepieces so the strings have indirect contact with the magnet. This has nothing to do with the springs.
The only ways to eliminate it are to lower the pickups where it stops, change to rails pickups, change to humbuckers, or use single-coils with the magnet on the bottom (like MIM Strats and Squiers - not recommended, IMO).