My ad hoc solution, which no doubt will be decried as cowboy work by the next owner, is to squirt in some silicone filler to hold the edges of the gib together and then put the screw through that, but I'm wondering if there's a better option.
Oh, it doesn't have to carry a large weight, the side that's screwed into the stud takes care of that, just not wobble or feel loose.



