Ahhh... well you need to put some foil on the pickguard (if the shielding isnt surrounding the whole system then the pesky interferance can get in and get nicely amplified by the high gain amp :(
however - its easy done, get some doublesided tape and some ali foil. cover the underside of pickguard, cut holes for pickups etc and then tape down - jobs a good un :) it should come into contact with the copper shielding, if it doesnt just tape a bit of foil to the copper and bend it over onto the body so the pickguard will sit on it - you may also need to put foil in the pickup cavities - again doublesided tape should do, and have it go over the edge so it contacts the foil on the plate... you should find this gives a dramatic improvement in noise :)
K