After you have your new hardwood plug in place and locate the butt plate in the right place, mark the location of the top hole carefully.
Remove the buttplate and determine the exact center of the hole.
Using a pointed scribe (or sharpened nail) place the point about 1/32 of an inch forward (towards the muzzle) of this marking and central to it side to side. Lightly tap the point into the wood.
Use a 1/16 inch drill to enlarge the little hole you made with the scribe. Then enlarge it using a 3/32 drill about 1/4 inch deep. Finally, use a drill that is the same diameter as the body (not the thread) of the screw in the threaded area to re-drill the final hole.
When doing this drilling, be sure to let the smaller holes locate the larger drill so the new hole will be in the correct place.
I like to then soap the threaded area of the screw (with Ivory bar soap) and drive the screw into the drilled hole to "tap" the wood.
After "tapping" the wood, remove the screw and replace the butt plate.
The slightly forward location of the screw hole should cause the screw to force the butt plate up tight against the stock.