Well, good luck. I would be inclined to try boat building epoxy rather than cyanoacrylate, simply because its much better at gap filling. I'm trying to think, though, of a good way of exploring what might be going on and where you would need to fill, and not coming up with any ideas I like. Drilling half a dozen 4mm holes round the affected area would certainly enable you to explore what's going on, but feels like a cure that is far worse than the disease. Does careful tapping with a pencil tell you anything useful in terms of the sound?