Wow, thanks to all for the thoughts and input. I'm attaching a quick photo of the bracket and screw in question. I'm not sure if I have the terminology correct, but this screw seems to be more of the "machine screw" style than the "wood screw" style; in other words, it doesn't have very prominent "barbs" along its length like a wood screw might; so I'm wondering if it might be effective to just go to the hardware store and try to find an actual wood screw of similar color, length and diameter, and see if that might snug in there with greater tightness?
IMG_20191113_083533.jpg
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