Okay, I messed up. When I drilled the butt plate it drifted off center, not really a problem as I could still put the screw in at a slight angle. Wouldn't look great but it would work. The real problem occurred when I drilled the pilot hole, the bit snapped off inside the hole with no way to dig it out without creating a fairly large hole.
As far as I can see I'm left with two options, one: buy a new butt plate and start over, two: drill a new hole and fill the existing hole in the butt plate with solder or pewter.
Any other recommendations would be appreciated.
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How about drilling out the broken bit and gluing in a piece of hardwood dowel to fill the larger hole?