Instead of a longer screw, take a couple of toothpicks, and cut them down to the depth of the hole. Coat them with a little woodworkers glue (Tightbond, or such like), and put them in the hole. Then screw the strap button on, before the glue dries at all. The screw acts as a clamp, and the glue will not stick to the metal.
I am assuming you have a striped out screw there, yes? This is, in fact, how most repair shops do these repairs, as most guitars do not have a huge amount of extra wood for longer screws.
I am not sure exactly where the truss rod on SG's goes to, but it would not surprise me if it was far enough to be an issue.
Light
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