I have had great sucess repairing door hardware holes with round toothpicks. Hinges and strike plates
take a lot of abuse and the screws get loose. I just give a squirt of yellow glue ( dries much faster than
white) and tap in as many TPs as it takes. Because they don't fit tightly together, you don't get
the hydraulic pressure that can happen with a dowel. Pushing a dowel into a hole with glue gives the
glue no place to go and creates pressure that will split wood, especially the crud that they make
door frames out of these days!
Since most toothpicks are birch, they hold up very well to taking a screw, and if Titebond 3 is used,
the whole thing takes stain fairly well.
I wouldn't use this any place out in plain sight, but under the buttplate it should give good results.