You need what is called an Escutcheon. They use them for bedding Action Screws in powder burner guns as well as plumbing and other applications. You can get them in different colors and materials. They are on Amazon and Ebay. You drill out the hole in the stock to a larger size and this metal cup type piece is epoxied into the hole. It has the correct size hole to keep the screw centered and is indented to sit slightly deeper than flush. You can also go to hardware store and get something shapped like that and drill it out to what you need.
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