Southern tip of Cat Island to Conception is just long enough to get lost without a GPS but nobody flies without one of these nowadays. Do they?
You're right, more likely mechanical, but bad luck not to find shallow enough water to be able to walk to safety.
Just a thought. How long would it take to be found if you went down in the undergrowth even next to the runway at Rum Cay. The "new" runway seemed to be in the middle of nowhere and deserted apart from a scrap flying boat.