A reasonable fix would be to dip a round wood toothpick in Elmer's (white) glue, then stick the appropriate amount into the hole. Let it dry, then reinstall the Schaller screw. The Schaller screws are much smaller than the Dunlop Straploks, so you might need to stick two toothpick sections in there.
Give it a day for the glue to dry before screwing anything in there (if the glue's not dry it will act as a lubricant instead of adhesive!).
You don't ever want to over-tighten a wood screw, but you do want strap buttons to be completely immobile, otherwise the little bit of play will allow the screw (which is under a lot of tension, probably as much as any on the entire instrument) to deform the wood that's holding it in. That starts a vicious cycle of causing the strap button to be looser, which makes it looser, etc!