Drill out the old holes twice the diameter of the original screw, which for the #10 screws used, would be 5/16" or 3/8". Drill all the way through the wood backing. Fill hole flush with White Marine-Tex, sand and buff out smooth and polished. Center punch the nice round filled holes, and re-drill for the #10 screws, It will be a lifetime fix, and no caulking is required since the screw is now totally contained in a waterproof epoxy plug. Cured Marine-Tex holds self tapping screws like no other product you can use.