I have in the past used s table saw to cut a very thin piece of hard wood, and then sanded it to fit. This is probably a little dangerous, hard to sand, and a pain to shape.
It's not nearly as good as Simon B's technique of laminating three or four pieces of veneer to the inside of the pocket. The veneer I have is between .4 and .5 I'd start with three. If still not tight enough ad a fourth and sand to the desired tightness. Sand the top edge flush with the body. After painting you won't even see that it's there.