How do I shift a door's latch hole and strike plate up or down half an inch?
If you can, glue a plug into the latch hole and similarly drill out the existing screw holes with a 1/4" bit and glue plugs of 1/4" dowel into them.

Now you have a blank slate to re-locate the strike plate wherever you want to.  Use a spade bit for the latch hole (3/4" or 7/8" or 1" - use the whatever is closest to the size of the strikeplate hole).