First of all, what is guitar spring noise? Look at this video to find out wether your guitar has it or not.
I've just seen this Instructable about guitar spring noise and I think my system works a bit better.
With my system (that I totally didn't invent) you can keep the stock appearance of the guitar, and avoid things like lint or getting the fabric to get dirty or lost.
Just take a small, flexible piece of hose (the ones employed to blow air into aquariums) and cut it to size so you can insert it inside the spring.
This works for every guitar with rear-mounted springs, be it a Synchronized or Floyd Rose tremolo. And it makes a HUGE difference, especially when recording.