I replaced the stock pickguard with an American Series one with the mounting holes. That way I can just stick a screwdriver through the holes to get at the screws.
You can try pushing the neck pickup all the way down with your thumbs and then slide the guard out from under the neck overhang, or else cut out some material on the pickguard where it goes underneath the fretboard. No one will ever see it, but you should then be able to get the guard off.
"I just sang a song parody, Dad. Like Weird Al Yankovic."
"Son, Al Yankovic blew his brains out in the late 80s after people stopped buying his records."