Thanks, Kevin. I was a little apprehensive on the first one but on the repeat, I just drilled the holes and ran the Dremel down through the slot in the old one to get it started. The right angle attachment gives good control of the blade because it just wants to pull away from you, not head off to the side.
Next time I have to cut one, I'll clamp something to it to act as a guide both for the angle across the pickguard and so the bit doesn't wander at all. New cutting blades are just big enough in diameter to go straight down through. Even if it canted slightly, a file can straighten the sides nicely.