I know that a wear plate from brass or iron is historically correct, but for the one repair that I did for a friend , I heat bent a thin piece of hard maple and glued it over the hole, then feathered the edges . The repair piece was probably only 2 mm thick when I started and less after clean up and sanding etc.
It shows as an obvious repair , same as the wear plates, but it's not cold on your hand in hunting season as the metals are. The repair was on the balance point of the rifle of this was a factor my friend wanted taken into consideration. It actually looks pretty nice .