And olde trick for installing a pachymar/padded butt to a modern rifle is/was.
A layer of Scotch tape (.002) under a layer of Painters tape (.005) under a layer of electricians tape (.006),,
,, all installed against the mating edge of the finished wood.
(and/or installed prior to the first cut)
As the install is shaped to contour with files/sanding blocks,, you work the edge until the "tape" is scuffed from sanding,
Remove one layer of tape and work down until the next layer is scuffed, then remove the next layer and work it down further.
That last .002 of the scotch tape isn't really noticeable at least with a butt plate install.
Just sending out ideas,,