I opened up the guitar when i first had this problem months ago and stuck aluminium tape all over the underside of the scratch plate and wired it to the guitars earth. This should give me additional screening too. (maybe it acts like one half of a capacitor plate now?) the bridge and strings are all earthed too.
You need to ensure the copper is continuous across the scratch plate and cavity, thus enclosing the major components in a cage
This is worth a read http://www.stewmac.com/freeinfo/Electronics/Shielding/i-3789.html and there is plenty of stuff on the web as well