A few weeks ago I played a gig in a large venue where the back wall of the enormous stage was covered in neon lights. My strat copy was picking up such a bad hum that it was totally unusable (I played the gig with my Les Paul copy) .
I spent $6.88 (US, on eBay) for a couple of 5cm X 3m rolls of adhesive backed copper foil. It took about two meters of one roll to line the wiring cavity and cover the underside of the pickguard so I should have enough foil left to do a couple more of these if the opportunity arises.
I've been putting off changing my strings or several weeks now because I was reluctant to get into this task but it was far easier than I anticipated. With luck, no more hum.